The exterior angles of a hexagon sum to 540 degrees.

A triangle ALWAYS has each exterior angle as 60 degrees.

The general formula for working out the mean exterior angle of an n-sided polygon is...

The calculation to work out the sum of the interior angles for an octagon would be...

180n - 360 is a generalisation that tells us the...

Generalising and comparing generalisations

﻿Hello and welcome to another lesson on Angles in Polygons: Angle Notation and Problem Solving. I just want to congratulate you if you made it all the way through the series, or if this isn't your first time, then welcome. But excellent, we're going to be moving on to our final lesson. So, without further ado, as always find that quiet space that you need in order to be able to concentrate, make sure that all your phones are muted and silenced that you can't hear those app notifications go off and indeed make sure you got yourself ready with your pen, paper and anything that you need in order to draw down angles which may or may not be a protractor or a ruler. Excellent. So, lets take it away with Mr. Thomas' lesson. So for the Try This, what I'd like you to do is to have a look as those tessellations. They've been made from regular polygons there. So what I want you to think about is how many different angles can you find that are not, aren't, 60 degrees, 90 degrees, or 120 degrees. How could you describe those angles? So for example, it's very very simple to be able to see that the square up there would have a right angle of 90 degrees. But, how could you make it so that it's a little bit more than 90 degrees? And give me a clue with my mouse there crossing over maybe to other shapes. Have a go at that task then please. Pause the video now and you'll have 10 minutes to do that. Off you go. And here, now if I were to work out what the interior angles of a hexagon would be That would be? What would it be? 720 degrees, good. So, if it's 720 degrees in total, then each of those of course is going to be what? What would each angle, interior angle be there? What would each interior angle be? Be 120 right? Which is why I suggested that 120 to begin with. But the point being is that we combined it with another angle. So we say this angle here of course would be 90. So, combining them together then the entire angle there would be 90 plus 120 which is? What would that be? 210 degrees right? So, we can combine all these together There's so many different possibilities. But one thing you may not have got is that you can have the exterior angle as well. So you've got the right angle there which is 90 You've got the equilateral triangle there which gives you 60 degrees up there So, you've got 150 like we discussed before You could also have the reflex angle in the exterior. So, if you have the reflex angle in the exterior, that would be 360 minus 150. Now, if you were to do that, what would you get? You'd get? 210, good stuff. So, 210 degrees for that one there. So, so many different options and possibilities you can have here and especially since I've got this bit here it should be a little be more apparent. This one for example, you have 120 degrees in the interior that then the exterior you're going to have? What would it be? 240, good. So, 240 degrees. Now, with that in mind, there are so many different ones I could be here literally forever, and ever and ever filling out angles and you know. Not literally forever, but you get the idea right? I'd be here for a very long time filling out all sorts of angles. So, I'm not going to do every single one, but you get the idea. You can play around with and get all sorts of answers. So, for your Connect today we need to really think about how we are going to talk about angles, and what we need to do in order to label angles. And there's quite a lot of naming conventions that go on with angles. So, we can talk about Angle ACD Now that pretty obvious but some of you may be scratching my head at the moment thinking, what does that actually mean? Well, what it means is that I'm going from A I'm going down to C, and then I'm going to D. So, if I create that, that sort of, that space there, right? I go from A, down to C, through to D. Then that forms a right angle of course. So, Angle ACD I could say is equal to 90 degrees. I could then also say angle, like this ACD. Notice that it's on the line like that rather than hovering, so that it's not looking like a Less Than sign. You can even make it slightly bigger, so that it really doesn't get confused there. So, Angle ACD is equal to 90 degrees. And then you could also have this Angle ACD, but with an Angle sign on top there. And that would be equal to 90 degrees. So, there's all sorts of different ways you could refer to an angle, and just be aware that those are the main ones that you would come across during studies. So, let's have a think about what other angles we could focus on. Well we could focus on this one here. Now if I wanted to focus on how I could refer to that 114 degree angle there, what could it be? Have a think about it just for a moment. What could it be? It could be BCE, couldn't it? So I could write it as B-C-E BCE rather than BCD BCE is, I want to write it like that now, is equal to 114 degrees. I could also have it as ECB. And that would be equal to, just put an angle like that. ECB would be equal to 114 degrees. I could then have What else could I have? I could have, Well could I have CBE? I couldn't, could I? Because if I did that, I'd be going from C through to B and then through to E. So, I'd be talking about the angle over here that's formed, which wouldn't be correct. So all I can have is BCE and ECB. But what I can do is I could refer to them in different ways. So I could refer to it as Angle ECB if I wanted to, and that would be of course equal to 114 degrees. So, so many different possibilities that we can think of there, alright? And then, I could also refer to this one up here. I know what that's going to be. I haven't marked that on, but I know what that's going to be, because what I can do is I can do 114, add 107, add 90 and if I do that, what do I get? Can you tell me, what would I get? If I did 114, add 109, add 90? Give you a moment just to think about it What would it be? Be 313, right? Go through there, carry the one. Got one plus zero, plus nine 10, plus 11 there so it gives me: one there, carry the one, three, 313. Now, if I do 360, subtract 313, will I get? What would I get? Seven would take me up to 20, so I would get 47, so 47 there. So, 47 degrees. Now if I wanted to refer to that angle there, or I could do for example: BCA, put angle sign on top. And that is equal to 47 degrees. I could also have Angle sign BCA again. And that would be equal to 47 degrees. So, I think you're starting to get the idea now. You just - you've got so many different ways to refer to them. There are loads of possibilities you can have there. So what I'd like you to do for your Independent Task is I'd like you to spend 10 minutes. All you need to do is you need to refer to those angles like I've done in that Connect Task. You've just got some different letters and different marked angles there. You even got one angle that you don't know, but you just learned how to do that, so nothing too tricky there. So, pause the video now, and have a go at that task. Awesome. Let's go through it then. So there are so many different possibilities you could have here. I'm only going to list out a few just in the interest of time. But, you may have well have a lot more. So, what I could do is I could have Angle ADC, like that. And that would be 48 degrees. I could also have Angle CDB. And that would be 58 degrees. I could also have FDB. And that would be a size of 80 degrees. I could also work out this unknown angle. If I add 48, 58, and 80 together, What do I get please? Shout it out for me. Not loud enough, what is it going to be? If I add all of those together? 228 degrees, right? So I could do 360 subtract 228. If I do that, what would that give me? That looks like it's 366, my apologies. 360 subtract 228. That would give me: 132 wouldn't it? So, I know that it's a 132 degree angle. So, it starts getting a bit more interesting now. I could refer to another angle there. I could refer to ADE. Angle ADE, and that would be equal to 132 degrees. I could refer to this one down here. I could do FDE. The angle sign on top of the D. And that would be equal to 42 degrees. And then I could do variations of them, and ultimately get the same answer. So, I'm sure you get the idea now. So, mark your work accordingly. Now for your Explore Task, I've got a really interesting challenge for you here. This one is taking what we've learned just a moment ago, and everything we've do so far into polygons, and saying: Well, if I wanted to refer to any of those angles there, how would I refer to them? What could I do in order to get to them? So, for example: I could refer to Angle DEI, DEI And that would be a right angle of course. So, you need to think about, what each of those angles would be. So, pause the video now. I'm going to give you 15 minutes to do that task 'cause there's loads you can do. Excellent. Let's go through it then. And if you need some help, I'm more than happy to provide it. So, we've got, like I said a moment ago. We've got that right angle there that I've marked. So, if I wanted to do size of DEI. That would be 90 degrees, wouldn't it? And that is the Angle DEI I could also have it as IED. The angle marked on top of there. I could also have it as Angle IED. And then we could also see it there, this square so I could have it as 90 degrees again for NJK. Yeah? So many different ideas there. Now moving on from the squares, I can refer to a really interesting angle here. I could refer to this one here. How would I do that one there? Think about that. That's going to be HIL isn't it? So, Angle HIL. Well that's made up of 90 there. Interior of there would be 120 degrees 'cause it's a hexagon. 90 there and then 60 here. So, the remaining angle, well that would be 180 going across there, 90 it'd be 270. That one there actually would be 90 degrees wouldn't it? So, that would be 90. So, it's another one that is 90 degrees. And then you can say any sort of ones that look like that as well would be 90 too. So, you could say GJK, would be 90 as well, right? And then there are the regular ones as well. The regular polygons that we kind of saw with the Tessellations that we saw at the start, right? So, we could do JFG. Angle JFG, and that would be 60 degrees. We could also do polygon here 120 degrees. Is that 120 degrees there? Am I right in saying that? Are we sure that's right, that's a pentagon isn't it? So, what are the interior angles in a pentagon? What would they be? Interior angle of a pentagon. Be 540 in total which means that each one would be 108. So, that one there would be 108, wouldn't it? So, we can correct that there. Would be 108. So, 108 degrees for that one there and that is BEF, so angle BEF can do with that one there. So, I'm going to stop there for now, but you can see there are other options. For example this one looks slightly different etcetera. So, all sorts of different answers you can have. I'm really, really happy if you manage to get a lot of them. So, as always, I'm really really shocked that we've come to the end of our time here. So, I really hope that you've learned lots about angles and polygons, and I'm sure you've absolutely smashed it. So, I'm really, really happy with everything you've done. So remember, take care in the future, and make sure you keep on learning. There are so many resources on Oak. Keep learning and doing lots. Take care for now. Bye-Bye.

Squares tesselate with each other.

Equilateral triangles tesselate with each other.

ABC is a triangle. Angle ABC is 90 degrees. Angle BAC is 23 degrees. Angle CAB is...

ABC is a triangle. Angle ABC is 90 degrees. Angle BAC is 23 degrees. Angle CBA is...

ABC is a triangle. Angle ABC is 90 degrees. Angle BAC is 23 degrees. Angle ACB is...

Angle notation and problem solving

In this lesson, we will learn about how to problem solve with angles in polygons, along with learning notations for referring to angles.

Maths

Y8 Maths

Key Stage 3

Year 8

Angles in polygons

Geometry

THEME

UNIT

Interior angles in a triangle

Categorising and defining polygons

Building shapes from triangles (Part 1)

Building shapes from triangles (Part 2)

Polygons and triangles

Generalising angles in polygons (Part 1)

Generalising angles in polygons (Part 2)

Finding missing angles in polygons

Exterior angles

Regular interior and exterior angles (and mean of irregular)

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

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

Which of the following statements most accurately describes an 'obtuse angle'?

A rhombus is an example of a...

Is it possible to have two obtuse angles in a triangle?

The total exterior angles of a polygon sum to...

The mean interior angle of a quadrilateral is...

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

The general formula for working out the total interior angles in a n-sided polygon is...

Lesson overview:Angle notation and problem solving

Core Content

Angles in polygons: