The total sum of the interior angles of two triangles would be equal to...

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

If I have a regular pentagon, what would the total interior angles sum to?

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

If I have a regular octagon, what would the total interior angles sum to?

Angles in polygons (review)

﻿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.

Angles on a straight line sum to 180 degrees.

Angles around a point sum to 180 degrees.

If a straight line contains 2 angles, one of which is 54 degrees, what is the size of the other angle?

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

Vertically opposite angles are never equal.

Straight line angles and angles around a point

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

Maths

Y9 Maths

Key Stage 3

Year 9

Angle review (9.5a)

Algebra

THEME

UNIT

Angles in triangles

Angles in polygons

Angles in parallel lines

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?

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.

Lesson overview:Straight line angles and angles around a point

Core Content

Angle review (9.5a):