﻿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.

The total sum of the interior angles in a triangle is...

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

In an equilateral triangle, each interior angle would be equal to...

If a base angle of an isosceles triangle was 34 degrees, what would the other base angle be?

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

Angles in triangles

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

Maths

Y9 Maths

Key Stage 3

Year 9

Angle review (9.5a)

Algebra

THEME

UNIT

Angles in polygons

Straight line angles and angles around a point

Angles in parallel lines

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.

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.

Lesson overview:Angles in triangles

Core Content

Angle review (9.5a):