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Hello, and welcome to another lesson on Angles in Polygons, exterior angles.

This is such an important topic it comes up time and time again.

Really important you're able to focus by silencing that phone of yours, making sure that the app notifications don't go off and that you're ready to learn because you're in a really nice open space where you're not going to be disturbed by anyone, including your brother, your pet, whatever it could be that's going to distract you.

So without further ado, let's let Mr. Thomas get on with his lesson.

So, before you try this, I will give you 10 minutes to think about what angle facts can you give me about those shapes? I've given you some prompts there already, you may be able to think of more, of course, but the sum of the blue angles are, and then the sum of an adjacent pair of orange and purple angles is? So have a go at doing that? See how many facts you can think of.

There are so many you could do for that.

Pause the video now, and have a go.

Cool, let's go through it then.

So, the sum of the blue angles, if we were to do that would be well, what do you notice? It's a one, two, three, four, five-sided shape.

So we can say it's a pentagon.

Now we can say the pentagon has how many sides, it's got five sides.

So therefore the total interior angles is going to be five subtracts three times by times, minus three.

Well mine about, minus two times 180.

So three times 180, which gives you of course, 540, very good.

So, 540 there.

So I can say the sum is going to be 540.

Goodness me, laggy computer.

540 degrees.

The sum of an adjacent pair of orange and purple angles, where we can clearly see that lies on a straight line, doesn't it? So I can say that that would be 180 degrees.

What other angle facts can I think of? Well, what about the orange angles here? One, two, three, four, five, six, seven, right? It's a one, two, three, four, five, six, seven-sided shape.

So if you were to work out the in the total interior angles of that seven-sided shape, you'd need to do seven minus two times by 180, and that would equal 900 degrees.

So I can say the sum of the orange angles angles, is sorry, are, well, what would the blank be there? Well, I've just said 900 degrees, haven't I, yeah? There are a few more that you could think of.

And actually what we're really focusing in on today is these exterior angles.

So these things here.

So when we extend that line out, yeah? When we extend that line out, we get an exterior angle.

So we want to extend an adjacent line out to ensure that it's going to be an exterior angle.

And that's what we're going to focus on today 'cause there's something very special about them.

So let's move on.

So if you're connect today, we're going to learn about exterior angles.

And it's the angle between a side of a polygon and an adjacent side extended outward.

Now there's something really special about exterior angles and we're about to find out what it is.

So I'm going to go off the screen just for a moment.

Don't you worry, I'm still here and I'm going to be helping you out throughout.

So let's go over to GeoGebra.

Okay, so we can see that we have a one, two, three, four, five, six, seven, eight-sided shape there, yeah? So that's an eight-sided shape.

And actually what we notice is, you're told this, the angles here are 45 degrees.

Now you may notice something straight away from that.

In case you don't, I just want to show you this quick illustration of what happens with these exterior angles.

Do you see that? What happens? Well, if we really zoom in, we can see that it forms around a point, doesn't it? Let's just watch once more, gets so close, look at it.

Gets even closer, and then it forms that point, doesn't it? So we can see it it works for any of these sided shapes.

Now let's go for a 12-sided shape, which give us 30 degrees for this.

And we'll get really close, expands out, gets closer and closer and it forms that point.

So it even works for say a triangle as well.

Right, you can see it's a triangle with a 120 degrees it goes like this.

How cool is that, right? You can zoom even further in.

I could watch this for hours, it's brilliant, yeah? Let's go and zoom in again, and there we go, good.

So difficult to get on the point, but you see the idea, right? So, that's the power of this exterior angles is that we know the total exterior angles sum to 360 degrees.

Let's go back so you can see myself and the rest of this show.

Now, for your independent tasks today, what I'd like you to do is to find the missing exterior angles in those polygons.

Bearing in mind that the total sum of those exterior angles is 360 degrees.

And you know that they lie on a straight line.

So, for example, for A you'd say, well 104 degrees, then I've got a straight line angle there.

So that's going to give me a total of 180 degrees.

So I know A there would be 760 degrees.

760 degrees, what am I on about? 76 degrees, okay? So, pause the video now and have a go at working out all those exterior angles.

Okay, excellent.

Let's go through it then.

So like I said, this one here is going to be 76 degrees.

This one here would be 99 degrees.

This one here, difference between 180 and 111 would be 69 degrees.

Difficult to do this off the top of my head but I'm trying to do it as quickly as I can.

This one here would be 45 degrees.

And, and then this one I threw in there because there's two ways you could do this.

You could either say, well, the total exterior angles are going to be 76, 99, 69, 45 added together.

Now, if you do those all added together, I'm just using a calculator to save us some time, if I add those together, I get 289.

If I do that subtracted, from 360, I get 71 there.

So I know F is going to be 71.

That then allows me to work out E which would be 109, very good.

So 109 degrees there.

You can also check your answer by adding all these together and they should give you the interior of a pentagon.

So if I do 109 added together with 104, 81, 111, and 135, I should get 540 and thankfully, if I add them all together, I do get 540.

So I know as a result of doing that, 540 degrees, I know I'm right.

I gave myself a little smiley face there, fantastic.

So, this one here, this one's a little bit harder just simply because there's more angles to work out.

Again, nothing too rocket science-based.

This one here is going to be 45 degrees, the straight line angle, 122, so eight would take me 230.

That would be 58 degrees.

This one here would be 63 degrees.

This one here would be 58 degrees.

This one here 56 degrees.

45 degrees.

This one here would be five 35 degrees.

And there we have it.

We can check our answer if we add them all together.

And again, just in the interest of time, I'm going to use a calculator that hopefully you can do it without.

But if you really need to, not the end of the world.

But if I add those together, lo and behold, I do get 360 degrees once I have some them altogether.

So I get that 360 degrees, which is great.

So I know I am right.

So mark your work right or wrong now, and do those corrections if you need to.

So, for your explore time today, I want you to think about the statements that you can make about those angles.

I reckon you should spend 10 minutes as usual on this task, to ensure you do it to a really good standard.

So pause the video now, unless you need help or want to go through the answers, and I'll be in the next slide to help you along.

So here I am to provide support or go through those answers.

Yes! Right, so the statements you can make about those angles.

We've got the green angles are the interior angles.

We can see them, they're contained within that polygon, right? The yellow angles are the exterior angles.

Make sense, yeah? That's the adjacent line that's going off from it, so we're happy with that.

The sum of the orange angles is 360 degrees.

You could also view them at the same time in some ways as the exterior angles, it's just, it's a different one, but as long as you're consistent the way you do it, it does make a lot of sense and it can also be an exterior angle.

The sum of the orange, blue and yellow angles is 180 times by six, because if you see they form a triangle, right? You could also say that the green angle and the yellow angle form a straight line angle.

You could also say that the orange and the purple form a straight line angle, yeah? So, so many different statements you can make about that.

So many that are, I imagine going to be right as well.

But it just allows you a little opportunity to explore and get a bit more comfortable with some angle facts that we've already explored so far in this series.

So again, I always say it time has absolutely flown by, and we are at the end of our lesson on exterior angles.

I just want to say a big congratulations to you at home for doing such a great job on that, if you're able to keep up.

And indeed, keep up that learning by doing that exit quiz and smashing it out the park to the best of your ability.

Really good stuff if you can do that.

For now, take care and I shall be seeing you.

Goodbye.