Numbers and numerals

Axioms and arrays

Factors and multiples

Order of operations

Positive and negative numbers

Expressions, equations and inequalities

Angles

Classifying 2-D shapes

Constructing triangles and quadrilaterals

Coordinates

Area of 2-D shapes

Transforming 2-D figures

Prime factor decomposition

Conceptualising and comparing fractions

Manipulating and calculating with fractions

Ratio

Percentages

Different number systems

Sequences

Forming and solving equations

Forming and solving inequalities

Linear graphs

Accuracy and estimation

Algebra and problem solving

Ratio (8.6a)

Ratio, real life graphs, and rates of change

Direct and indirect proportion

Univariate data

Bivariate data

Famous maths problems

Angles and parallel lines

Angles in polygons

Bearings

Volume and surface area of prisms

Area review

Circles

FDP review (9.1a)

Probability

Sets and Venn Diagrams

Solving linear simultaneous equations algebraically

Solving linear simultaneous equations graphically

Angle review (9.5a)

Constructions, congruence, and loci

Pythagoras's theorem

Ratio review (9.7a)

Similarity and enlargement

Surds and trigonometry

Quadratic expressions (9.9)

Quadratic equations (9.10)

Indices and standard form

Growth and decay

Finance

Maths

Y9 Maths

Key Stage 3

Year 9

Algebra

THEME

UNIT

In this lesson, we will review that the internal angles in a triangle sum to 180 degrees.

Angles in triangles

﻿Hello, and welcome to this online lesson on Angle Review. The first one in the series, Angles in triangles. I'm Mr. Thomas, I couldn't be happier about teaching you today. We've got so much we can learn about angles and triangles. It's going to be a fairly short lesson because there's not a huge amount that we need to cover, but it's really important you understand everything that we're doing. So remember, turn your phones off, make sure they're nice and silenced that you can focus and concentrate unless you're watching from it of course, where you've got the app notifications all nice in size, so you are not disturbed. Make sure you're in a quiet place as well. You can really, really concentrate and do that maths that we need you to do. So without further ado, let's take it away. So if you'll try this, what I'd like you to do is with your pen and paper, of course, find the missing angles in each of those triangles. So copy them down and have a go at doing it. I'm going to give you five minutes to have a go at working out those missing angles. I provided some support for the first one. So it's a basic idea of how to do that, off you go. I give you five minutes. Excellent. So let's go through it then. So I've given you a little bar model there of how we can do this. There's one idea that you can do that way if you like it. Because we can say that all the angles sum together to give us 180, the total interior angles and trying to sum together to give us 180 degrees. So a plus 50 plus 34, give us 180. What we can do is we can subtract 34 Of course and 50 from 180. So if I do that, I'm left with of course a is equal to 96. So I can get a is equal to 96. I can cross off each individual amount, then subtract 34, subtract 50 from the amount there. And then I'm left with of course 96 over here. And that is what a is equal to of course. Same idea for this one here, where I could draw a bar model if I wanted to. I could have b here, 43 and 19. And that of course is equal to 180. So what I recognise is I can get of course, b plus 43 plus 19, or 43 plus 19 would give me 62. So I need to subtract 62 from 180, and I get of course b is equal to 180 subtracts 62, what would that give me? What would that give me? 118, very good. So 118 degrees. Remember these degrees throughout as well. And this of course is a right angle. So it's going to give me 90 degrees. So I can do another one. So I could do, c here 90, and then 27. And that of course is equal to a 180. So what I can start to do ,is I can do 90 plus 27 to simplify that, which would give me 117. I can then do 180 subtract 117, which would give, what would that give me? Very good, 63. So, c is going to be equal to 63. So you can mark your work, degrees of course. You can mark your work right or wrong now and do your corrections if you did get them wrong. I will be moving on in just a moment. Excellent, let's go on. So if you're connect, I want us to think about these because these are very special type of triangle. This is an isosceles triangle where the sides are the same length. And that means that angles at the base of this triangle, so this is the base of the triangle, are equal. So that means this would be 67. So with that in mind, I can do another bar model if I wanted to. What that is, is going to be 67, 67 and then d. So if I do that, I get 67 and that of course is equal to 180. Because the total interior angles in a triangle sum to 180 degrees. So I can do 67 plus 67, and that would give me 134. Subtract it from 180, What that gives me, what does that give me? Gives me 46, doesn't it? So angle d is going to be equal to 46 degrees. What about this one though, What we've got e and 103, but we know this is the base, right? This is the base of our triangle, because we've got our two equal sides there, and our base is at the bottom there. So we know that's going to be e, that will be e, and then this one here would be at 103. So that is equal of course, in total to 180. So when I do that, what I get is I get, well, if I do 180 subtract 103, I'm left with a slightly different amount. I'm left with a condensed bar model there where I've got e and a, and I'm left with 77. Now I need to distribute evenly 77, between two lots of e. So I need to divide it by two. And what I'm left with then, is e is going to be equal to 38.5 degrees. Excellent work if you got that, without me having to necessarily help you. Now, this is an equilateral triangle. Because I can see all the sides, can even write that down, equilateral. So that's an equilateral triangle. Now what that means is all the sides are same length. So all the angles are the same size as well. So that's going to be f and that will be f as well. So I know that if I add those together, I'll get f plus f plus f gives me three f. I know that three f or simply f plus f plus f, is going to be equal to 180. So I can say even more simply, I've just got three blocks of the f, would be equal to 180. So if I want to distribute 180 evenly between three lots of f there, what I can do is, do 180 divided by three, what I get is f is equal of course, to 60 degrees. Very good if you got that. Let's move on then. So if your independent task there, what I'd like you to do, is to find all those unmarked interior angles in each of those triangles below. So you need to find that one, for example, this one here, this one here, and then these two here. So pause the video now, and have a go at that task please. I will give you 10 minutes to do that. Okay, excellent. Let's keep going. So your answers are as follows then. So for this one, you're going to do 180, because the bottom we know all of them sums to 180 degrees, and we know that this one here would be 35 ac, and then I'm going to call that x, the thing that we don't know up here, what this would be. So, as a result of doing that and doing all the calculations that we should have done, we will get, of course, what would we get? x being, x is equal to the unknown. What would that be equal to? 65, wouldn't it? 65 degrees. Very good. It is 65 degrees for that one that there. This one's a right angle. So we know if we sum it up, so far we've got 440 degrees. So this one here would be 40 degrees when we follow that process. This one here, again, very very similar in a lot of ways, this one here is going to be 140 when you do the sum. So you subtract it of course, and you get 40 degrees. This one is a little bit nicer in some ways, actually. Because you can fill in that angle there, which is quite satisfying to fill, which is going to be 70 degrees, because those angles at the base of the triangle are equal. So then we discover, of course, this one here would be 40 degrees, as a result. Very good if you've actually get these. Look back at the work that we did in the previous connect part, just in case you don't fully understand that, and you need to go through it again. So if you're explore, what I'd like you to think about is these two statements here. That, are these triangles even possible? I'd like you to justify your answer. So you pause the video now. I'm going to give you seven minutes to have a think about that, and try and maybe draw them out. If you're a bit confused I can provide support or go through the answer in the next slide. Off you go. Very good, so let's go for it then. So try and go with one line of symmetry and one angle of 174 degrees. Now it's going to be very difficult for me to draw this accurately, it should be because I'm drawing with a freehand. It's very difficult for graphics parts to be able to do that. But, what it would look like, it is actually possible right now, what we need to do is we need to do something that looks like this. And then just to be really, really sure, that again, is we say that these sides are equal because this is going to be an isosceles triangle. Because if I cut it down the middle there, we consider that as a line of symmetry. That's one line of symmetry, if I do the isosceles triangle apart then. So I can't cut it any other way and it be equal on both sides, equal components, right? If they are folded that would have mapped perfectly, it would for that one line of symmetry there. And then I can do an angle of 174 degrees the top, which it means that each of these would be three degrees and three degrees. So like I said, not drawn to scale, not to scale, but you get the idea that, that would be the triangle that needs to be drawn. An equilateral triangle with angles of 70 degrees. Now that's really interesting. There's only one possible, equilateral triangle. And we said that we had it just a moment ago, didn't we? With the example of f, f and f. And we said, each angle had to be 60 degrees. So that is not possible. Nice try there. I just want to say absolutely brilliant work so far, and it brings us to the end of the lesson. So hopefully you've got a good understanding now, how do angles in triangles in interior sum, of angles sums to 180 degrees. You really understand going forward. In our next time, we're going to explore another angle fact. So stay tuned and smashed the exercise quiz so you can move on to our next lesson really well. For now take care and I shall see you soon. Bye bye.

In this lesson, we will review that the total interior angles of polygons are made up of many triangles, and that this relationship is determined by the number of sides the polygon has.

﻿Hello, and welcome to this lesson on angles in review, angles in polygons. Really important that you're able to focus fully on this lesson, so make sure those phone notifications are silenced and that you are concentrating fully in that quiet space that you may have found in order to access the work to the best of your ability. As always, we're going to do some very, very powerful maths, so make sure that you are concentrating well. Make sure you've got that pen and paper in front of you so you can do all your workings, and you may even need a calculator if you want to speed up the process. So with that in mind, let's continue with Mr. Thomas' lesson. So, if you would all try this. What I would like you to do, is I'd like you to think about how you can prove the idea of what the interior angles in a quadrilateral add up to. Seems quite simple. Is it? Have a go at it, I'll give you five minutes. Pause the video now, and have a go at it. Very good. Let's go through it then. So do you remember the idea that we need to go from one specific vertex and we needed to split it into triangles? So building on that idea, that we learned in the previous video about the interior angles. In a, in a triangle. Some 280 degrees. Well, 180 degrees here, 180 degrees here. So we know the interior angles in a quadrilateral- in a quadrilateral, goodness me. My uh, my words can't come out today. Um, that would be equal to 360 degrees. Very good. So, thinking about how we can extrapolate that onto more complex shapes, where we've got more sides. Well, we just go from one specific vertex. So for this, one, two, three, four, five sided shape. A pentagon. And what we can do is split it into one, two, and three. So 180, 180, and 180. So we get a total of 540 degrees. It's my interior angles in that polygon. I can then, for this six sided shape, all right? This hexagon. I can do one, two, three, and four. So 180, 180, 180, 180. So then that gives me, if I add those all together, what would that give me, if I add all those 180s together? That would give me of course, 4 lots of 180, what would that give me? Would give me 720, wouldn't it? So you're starting to get the idea and we use this formula to help us, don't we? We can see all these triangles fine. But actually, there's a really really helpful formula, because it's quite a lot of hassle in order to be able to do these all the time, right? It's very mechanical, uh starting to get a little bit bored of the fact that I've got to do that every single time. What we notice, though, is that we've got 6 sides here, for example. Right? And we've got four triangles. So I know the amount of triangles that I have is, n minus 2, amount of triangles. And I need to multiply, of course, by 180. Don't necessarily have to have that multiplying but it's just helpful to know what that means. So I follow that formula, 180, times by 'n' subtract 2, where is 'n' is the amount of sides of the polygon. So, if I know this has one, two, three, four, five, six sides. I know it's going to be six subtract two it's going to be four times 180. And that gives me, of course, 720 degrees. And I know that's right because I've already done a six sided shape there. Yes, very good. Let's move on then. So for your independent task, here, what I'd like you to do is to use that sum of the interior angles, to have a go now at working at what those missing angles would be. So for example, that's going to be a quadrilateral, sums for 260 degrees, so you know that missing angle is going to be the difference between the total sum there, and then of course that missing angle would be the difference between that 260 subtract um, the total. Same idea for these sorts of questions over here. So pause the video now, I will give you 8 minutes to do that. Off you go. Very good, let's go for it then. So if we add up all those angles there, so far, we get 66 plus 96 plus 63. So that gives us 225. Now you could have a very long bar model modelling that, but for the purposes so far, I'm just going to do 225. We know the total exteriors, sorry interiors, is going to be 360. So I'm going to have to do 360 subtract 225 and that will give me A. So when I do that, I know that 'a' is going to be equal to, what would 'a' be equal to? It will be equal to 135, very good. So 'a' is going to be equal to 135 degrees. 'b' is a very similar process, I know it's a four sided shape here, so what I need to do for this one here, is I need to add up all those so far, so if I add those all together, I get uh, 150, 171? Yes, 171. So, I need to do 360 subtract 171, and that gives me 'b'. So what I get if I do that is, what do I get? Nice and loud please, shout it out. What is it going to be? 189, right? Very good if you got that. If you didn't, think about why. So, 'b' is going to be equal to 189 degrees. This final one's a little bit more complex, but we know it's going to be a one, two, three, four, five, six sided shape. We've done that before so it's going to be a irregular hexagon. So it's not a regular, 'cause regular means that it's all the same sides. Uh, all equal sides. Irregular means that's it's not necessarily all of those equal sides. So what it's going to be, it's going to be four, cause six minus two, six sides times 180. So, times that by 180 and we know that's going to be 720 degrees in total. So if I add up all those uh, all these angles here that I have circled. What I get is 98 plus 142 plus 113 plus 107 plus 130, that gives me 590. So, what I need to do, 720 degrees subtract 590 degrees, and that gives me of course 'a'. So therefore I know that 'a' is going to be equal to, what is 'a' going to be equal to? Very good. 130 degrees. Nice. Mark your work right or wrong and do corrections if you do get them wrong. So what I would like you to think about now is explore task. It says Antoni and Xavier are arguing about who is correct. Who do you think is correct and why? So I've got Xavier saying 'It is possible to draw a six sided polygon in which all interior angles are 108 degrees. Let's see. 'It is possible to draw a five sided polygon in which all interior angles are 108 degrees.' Who knows? Pause the video now, I'll give you five minutes to have a think about and play around with that now. Cool. Let's go through it then. So, the six sided shape then. So let's, let's do it. So all the interior angles going to be equal. That means it has to be regular. So it means that all the sides have to be the same length. Now, I'm not going to be able to do it totally accurately. But we get the idea. If we do a six sided shape, it's going to be something like this. Two, three, four, five six. Okay, so that's my regular polygon there. Okay. Um, if I do that then, I need to think about what triangles I can split it into or I can split it or I can use the formula. So I can do 180 multiplied by n subtract two, so six minus two which gives me four. So, 720 degrees. I then need to split those angles equally between it all. So I need to do 720 divided by six, right? Now, if I do 720 divided by six, what do I get? Can you tell me, what do I get? I get 120 degrees, wouldn't I? So if I wanted to split them all equally, I'd get 120 degrees for each of them, wouldn't I? Etcetera, Etcetera, Etcetera. Now, that clearly is wrong it's not possible then, as a result of doing that. Let's check uh, sir Antoni's argument then. Well, this one is going to be a five sided polygon, so it's going to be a pentagon. So one, two, three, four, and then five. So, that of course is a different uh, length of line to what we've had previously so we're just going to do a double dash. Now, what I can say about this one is I'm going to do 180, multiplied by n minus two, well in this case it's going to be five minus two, which is three. So that would be 540 in total. Now I need to difference between one, two, three, four, and five angles. So I need to do 540 divided by five. If I do that, what I get is? Ah, seen something haven't you? It's going to be 108 degrees. So I know that each individual angle here is going to be 108 degrees. So actually, we've proved Antoni to be correct. Very good if you got that without me having to help you. But even if I did help you, very good if you understood it. Well done. So that brings us to the end of our session here today. I just want to say a big congratulations if you've managed to keep up. Make sure that you smash that exit quiz and that you stay tuned for the next one in the angle series. For now, take care, and I shall be seeing you soon. Bye bye.

In this lesson, we will review how straight line angles sum to 180 degrees, and how angles around a point sum to 360 degrees.

Straight line angles and angles around a point

﻿Hello, and welcome to another lesson in our series on "Angles Review." This one is on straight line angles and angles around a point. So as always, I want you to make sure you've got your pen and paper ready to write stuff down on and you've got your nice quiet space that you can relax, and you can really make sure you focus on the math, 'cause it's really important you understand that in order to access the rest of the curriculum. So without further ado let's make sure that we go ahead and start our lesson, Mr. Thomas. So if will try this, what I'd like you to do is without a calculator, have a go working out the following, filling in those blanks. And then when you think a little bit deeper as you're going through the exercise and thinking why I have chosen some of those numbers as part of your try this? Why will we be using them a lot in today's lesson? So have a think about that throughout why I would have chosen those numbers and think about what specifically it's going to come, why it's going to come up in today's session? So pause video now, have a go to that for five minutes, please. Off you go. Awesome, let's go through it then. So 90 plus something is 180. That's going to be 90 of course, mark it right or wrong, please. 30 plus something is a 180, that's going to be 150. 180 minus something gives you 70, that'll be 110. So mark these as you're going along, please. Four times something gives you 180. That one's a little bit harder, what could that be? Well, that'd be 45 so mark it right or wrong. 80 plus 120, plus 120 gives you 360, well, 80 plus 120 is 200, 320, so you're going to have to add on 40 to get to 360. Nine times something equals 360. That would be 40 there. And then the final one, 360 minus 150 would equal to 110. So mark them as you're going along. If you're confused about how to get them, think about the inverse, think about opposite. So if I wanted to get knowing 90 plus a blank, you call that X for example, and then you could subtract 90 on both sides and you get out 90. 30 there, opposite of adding 30 would be subtracting 30. So subtract 30 from 180 you get 150. Opposite for example, here would be dividing by four. So 180 divided by focuses 45, et cetera. So why would I have chosen these well, we know number one, that they are the angles in a straight line, do you know what they are? Sum to straight line sum to 180 degrees. Don't they? Right, very good if you managed to get that. And the second idea of 360 here, rather than the 180 we've been using is that angles around a point sum to, 360 degrees. So very, very good if you must have realise that was why I was getting at there. So I'd take him over now to write that down, please. So with that in mind, let's continue. So what I want us to think about is these straight line angles. Now the first one we've got 112 degrees here and a. So what I'm going to have to do is I'm going to have to form a little equation. I will do 112 add a is equal to 180. So I've got that 112, plus the blank of a is going to be equal to 180. So I can subtract 112 on both sides. And what I'm left with is a is equal to 180 minus 12. What would that be pleased? 180 minus 12. Come on, shout it 68, isn't it? Very good so we can say that 68. What about this one here? Where we've got b and b. We know they're going to be equal. They're both b, then they're going to be equal. So we've got 136, plus b, plus b is equal to 136, sorry 136, 180. So 180 degrees. Cause it's on a straight line of course. So with that in mind, we can then begin to subtract 136 from both sides. And if I do 180 minus 136, I get a b plus b is equal to 180 minus 136. But would that be please? Shout it out, Connie even louder. 44, right good. So 44 for that one there. Now you can say that 2b equal to 44 and then therefore b is equal to two 22, sorry. Or you can say that well, something out something, and there's some things the same are going to be 44. So I can say that very simply b is going to be equal to 22. There we go, good. So that one, that's that dealt with and this one's out with here. The angles around a point though, well, we need to some angle facts here. We can say that c is equal to 65 cause vertically opposite angles are equal. And then we noticed that actually it lies in a straight line doesn't it there. So this one is going to be the straight line form there. So to get from 65, up to 180, you can do 180 subtract 65, find the difference between them. And you know, that's going to be 115. And then you can also say that if the opposite angles are equal for this one here, so vertically opposite angles are equal just to shorten it there. So that's going to be 115 degrees there. You can check your answer by adding it all together. So if you add all those together, lo and behold, you get 360 that magic number. And we know that to be true because we've got two straight lines here we've got this part here and this part here. So that would altogether two times 180 would give us 360. So we know we're correct by doing that sum up. So fairly intuitive what to do then nothing too tricky just to recap of what you've known so far throughout your studies. So with that in mind, I'd like you to have a go at that independent task for me, please. So pause the video now and take as long as you need. I imagine it would only take eight minutes to do that. So have a go and check your work for out and make sure it's exemplary, off you go. Awesome, let's go through those answers then. So what we can start to do is we can start to form an equation here. So 54, plus a, plus 61 is equal to 180. Now, if I do 54 plus 61, what I get is of course, fill in that blind for me, what would it be? It'd be 115, wouldn't it? So 115 plus a is equal to 180. Now, if I do subtract 115 on both sides, what I get is of course, 65 very good. Is equal to a, mark it right or wrong please. This one here, this one I'd probably say is the easiest one here. What we've got is 180, of course it's a straight line angle. And then of course we have 43 plus b. So 43 plus b is equal to 180. So if we subtract 43 on both sides, b is going to be equal to, what would it be? 137 excuse the pen of course. So we have that one there mark it right or wrong. So both of those were straight line angles. And they sum to 180 degrees as a result. And the same for this one here. So it's a straight line angle, which sums to a 180 degrees, excuse my shocking writing there. And so we can say 28 is a vertically opposite angle. So there's going to be 28 degrees. You shouldn't shorten yours, but I'm just doing it in the interest of time. And the fact that I've got quite a lot of writing there. So what I can start to do there is I can say, well, this is 90 degrees because that's a right angle I'll shorten that to RA. And then I know this is a straight line here. So this straight line here means that 90 plus 28 is going to give me 118 in total. And the difference between 180 subtract 118 would be two will take me 220 so 62, right? So I can say f is going to be equal to 62 degrees and then follow that through. Well, vertically opposite d is going to be 62 degrees as well cause of vertically opposite angles. And then we can say, well, e is vertically opposite to the right angle. So 90 degrees there again, because it's a vertically opposite angle. We can check it by adding it all together. Now, if you add all those together, you would of course get 360. So you can check that, but I've just done it mentally already. I can see it's going to be 360 cause all the angle around a point sum up to 360, and I've done it and I know. So just check your answer by doing that. So if your explore task day, what I'd like you to consider is whether the following statements are true or false. And also why would they be true or false? So pause the video now and have it go at that for the next eight minutes, please. If you need some help or you want to go for the answers, I'll be available in the next slide. Very good, let's go through it then. So we've got this student over here saying a plus b is equal to 180. Now we know that it lies on a straight line. So yes we know that's true, lies on a straight line a plus b, a and b rather lie on a straight line. What about 65 is equal to b? Well, unfortunately that's not true because it's a straight line there. So this part here would mean that the 65 there is vertically opposite to a, but it's not with b. So that one that isn't true. It would be 180 subtract 65, which is equal to 115 instead degrees of course. What about this one over here b is equal to c. That's true because they are vertically opposite angles. If you look at the diagram b is equal to c you can see that, they are vertically opposite around that vertex that are intersection. What about 130 plus 2b equal to 360? Well, you can say because b is equal to c you can say that with that would be b. So that would give you 2b, cause you're doing b plus b, which should give you 2b and then 130, 65 well, we know that to be 65 as well. So plus 65, plus 65 that would be 2b plus 130. And that would give you the sum of the angles around the point, giving you 360. So we know that to be true, that's really, really helpful. So that's probably the hardest one there to realise. And if you've got that, that's really impressive. So well done. So that ends today's lesson. I just want to say really, really well done if you've kept up with that really important you're able to review that cause it comes up all the time in math, those sorts of things to do with angles. So very, very good if you can recap and smash that exit quiz as always. So for now take care and I will be seeing you, goodbye.

In this lesson, we will review the various angle facts that appear with a transversal and parallel lines.

Angles in parallel lines

﻿- Hello and welcome to this online lesson on angle reviews, angles in parallel lines. So without forever ado, what I'd really like you to do is to make sure that you've got that quiet space that you're in, that you can really concentrate, you can really learn and make something of this lesson. This is our last one. So final push on, let's go for it. So make sure there's app notifications are silenced, that you've got your pen and paper to hand and if you've got one, that you've got your laptop ready and you've got everything ready to go and you're not gonna be disturbed for the next 10 minutes or so. So without further ado, let's take it away with Mr. Thomas's lesson. So for your try this today what I'd really like you to do is to think about the intersection here that's formed by two lines crossing. I want you to think about what facts you can write down about any four angles formed by two straight line crossings that you see there. So, with that, I want you to spend five minutes now pausing the video and having a go at that task. Off you go. Excellent, let's go through this try this then. So the ones that I thought of were the following. I thought of vertically opposite angles are, what are they? They are equal, aren't they, very good. Vertically opposite angles are equal. So I can say that those two angles there are equal. And I can say that those two angles there are equal. I also thought of this, what am I indicating there? Angles on a straight line sum to 180 degrees, right? Very good if you got that. And then finally, I'm gonna mark that point there, why am I marking a point? Well the reason why is because angles around a point sum to 360 degrees. Very good if you managed to get that, reason being, see that other straight line there? Cause the angles there are two times 180 degrees, which gives you 360. Awesome work for manager to get that. Let's move on, for our connect today then, what I want us to consider is the alternate interior angles and then alternate exterior angles. So do you see this? Remember this is the interior region that we talk talk about and this is the transversal that cuts across them, right? So we've got alternate interior. As you can see marked there and alternate interior just here. They're on opposite sides of that transversal and they're both in the interior region. Same here, but it's just the exterior region this time. So you've got exterior there and then the exterior angles just there. So we can see that they are of course equal, they're equal to each other. There we go, each other. So alternate angles are equal. Very, very, very, very, very, very important justification. So with corresponding and allied angles, what happens is they lie on the same side of a transversal. So you can see there, they can lie on the same side and they're in different regions. We see this one's in the interior region and this one's in the exterior region, right? What about allied angles? Well, do they look equal? We can see the allied angles sum to 180 degrees. What about corresponding angles? Well corresponding angles are equal. So just be really, really aware of that, that the allied angles you can clearly see sum to 180 degrees and then corresponding angles are equal. So with that, what I'd like you to do here is for your independent tasks, to find various angles there that are equal to each other for corresponding and allied in particular. And then I'd like you to think of as many pairs of angles as you can find that are equal to each other. And you can add to give you 180. Okay, so pause video now, I'm gonna give you nine minutes to do that. Off you go. So let's go through our answers then. So for the pairs of corresponding angles that I had, you could have G and C and they would be equal. Of course. You could also have F and B, you could also have H and D, they would be equal to each other. And then you could also have A and E. They'd also be equal to each other. So there's quite a few different options you could have there. Really good if you manage the spot some of them. And then the allied angles, well we know that C plus F would some give 180, they are allied. We could also see of course that we've got D plus E. We've also got E plus G some 180 degrees. You've also got which other ones, if you've got B and G, what else have you got? You've got H and E, A sorry, haven't you? H and A. Very good if you managed to get that and then that is it from what I can tell. So very, very good if you managed to get some of those or all of them indeed. Very, very good. So for your explore today, what I'd like you to do is to use your knowledge from this lesson to find and justify the size of unknown angles in that diagram below. So pause the video now, I'm gonna give you 10 minutes to have a think about how to do that and you can have a go to the best of your ability. If you're still struggling or wanna go through the answer, I'll be available on the next slide. Excellent, let's go through the answer then. So I can say that this is gonna be equal to 110 degrees. 'Cause I could say vertically opposite angles here. I could also say that C is going to be 70 degrees 'cause of this straight line. I could say that A is gonna be vertically opposite so it's gonna be 70. I could say that this J over here would be due to allied angles. I could say that that would be the case. That would be 110 degrees. I could also say it correspond with that one there as well. There are loads of different justifications, as long as you're using the correct angle, the very one that you're focusing on, then it's totally valid to do a lot of them. I could say this one of course is allied with D down there, so that's gonna be 70 degrees. I could also say on a straight line here. I could then go vertically opposite here with I. That is perfectly acceptable. And then a straight line if I wanted to here. Very good if you've got justifications around what we've done in today's lesson with regards to allied and corresponding, et cetera. So for example, K could be corresponding with D down there. A could be corresponding with I. You could also have, if you really wanted to branch out the previous lesson, not in the remit of this, but if you wanted to branch out, you could say J is alternate D, et cetera. So there's so many justifications there which are really good if you've got that, well done. What about this one? Well we can say this one here is gonna be vertically opposite, 32. With the 32 there, we can say this is gonna be vertically opposite, give us 30 and then we add them together, which gives us 62, subtract from 180, which would give us, what would that give us? M is equal to 118, right? Very good if you managed to get that, really, really clever 'cause of the interior angles in a triangle we can then say this bit here would be 118 degrees 'cause it's vertically opposite. We can then say, down here we've got a corresponding angle, which gives us 30 degrees for that bit there. We can then say, what could we do from there? Well what we could do is we could say that this, N, corresponds with the 32 just there, couldn't we? Or we could say angles in a straight line. Very, very good if you managed to get that. And then this one here we can say of course that it is vertically opposite with the 30 just there. Very, very good if you managed to get that all without my help. So I just wanna say, that's the end of our lesson and I'm just really, really amazed if you managed to keep up with all that. 'Cause it can be a little bit tricky at times just realising, oh, is that an interior, is that exterior, is that alternate or is that all sorts of things that kind of come up and corresponding, et cetera. So if you've managed to keep up and you think, yeah, I've got this. Cool, thank you so much Mr. Thomas, I just want you to potentially ask your carer or parent at home if they can get permission in order for you to share your work. It'd be really amazing to see so much work. You can tag us @OakNational and may even be able to see some of your work. Be amazing to see loads of your stuff that you've done. So make sure you smash that exit quiz that you do such a good job and prove to everyone that you've done such a great job by getting five out of five in that exit quiz. From now, it's goodbye for me and stay safe. Bye bye.

Angles on a straight line sum to 180 degrees.

Angles around a point sum to 180 degrees.

If a + b = 180 degrees, then 2a + 2b = 360

Vertically opposite angles are never equal.

A right angled triangle with one angle as 23 degrees would mean the remaining interior angle would be...

If the base angles of an isosceles triangle were 34 degrees, what would the unknown angle be?

If I have a regular pentagon, how many triangles from one distinct point internally can I create?

If I have a regular octagon, how many triangles from one distinct point internally can I create?

Alternate interior angles are equal.

If I know Angle A and Angle B are allied angles and Angle A = 60 degrees, what is Angle B?

Corresponding angles are equal.

An intersection is the point at which two lines never meet.

Unit Overview: Angle review (9.5a)

Lessons:

Angles in triangles

Angles in polygons

Straight line angles and angles around a point

Angles in parallel lines