Lesson video

Hello, and welcome to this online lesson about angles in polygons.

This is the first lesson that I'm going to be teaching about.

It's about interior angles in triangles.

My name is Mr. Thomas and I could not be happier about teaching you angles in polygons.

It's a really amazing topic.

I really, really hope that as time goes on, you appreciate that as well.

So for today's lesson, you're going to need the following.

You're going to need a ruler, you're going to need some pen and paper, and this one other thing I've forgot.

What was it? Ah, there we go.

Right.

So we're going to need a pencil and a ruler cause we're going to be copying down some triangles.

So it's really important that you follow along and you take notes and that you are copying down what I'm doing on my screen.

So please, take a moment now to clear away any distractions, to get those materials that you may need and get your brother and your sister out of the way, right? Or your pet, okay? We don't need them just now.

You know, your pet hamster can have a cuddle another time, your dog can be stroked and other time, et cetera.

So let's just remove those out, okay? And then just think about what we really need to focus on, which is the Maths.

So we need to find a nice quiet space as well, away from any distractions, we need to turn the notifications off from our phone.

So I've turned off my notifications off my phone, really important that you do the same.

So I'm not going to be distracted whilst I'm doing this video for you guys.

You need only to be distracted from me talking as well.

Really important you're paying attention.

So with that in mind, what I want us to do is to focus on that really, really important Maths and to keep going as we go along and keep up with what I'm doing.

So what I'd like you to to do now is I'd like you to have a go at the try this.

Now Binh is saying the angles in each of these triangles, sum to 180°, therefore, the sum of the angles in the total shape is 360°.

Do you agree with her? Do you disagree with her? Have a go at it now, pause the video please.

Okay, let's go through the try this then.

So she said that statement, do we agree with her? You may have said, "Yeah, actually I do agree with her," because of course the angles in the triangle, stays 180°, that is 180°.

But can we think actually for one moment, "Hmm, that could be wrong actually, Mr. Thomas, that could be wrong." Why could that be wrong? Well, the reason why is because if we think about the sum of the angles in the total shape, well, surely if we add those together, we get 360.

So yeah, we've actually proved to her correct there.

So she's both incorrect and correct at the same time, it's a weird paradox.

It's sort of like, just doesn't make sense.

Let's go on to explorer.

So like I said, the triangle here sum to 180°, the interior angles in that triangle sums to 180°, the interior angles in this triangle sum to 180°.

But then if we add that together and we get the total, the total interior angles of those triangles, that gives us 360°, right? If we do 180, of course, plus 180, that gives us 360°.

However, we're thinking at this point, "Hmm, I'm not really too sure," because if I then consider the larger triangle, just here that I've highlighted with my red pen, right, if I consider that there, what I'm going to get is just these vertices here.

So I get that top one, get that one on the bottom right, and I get that one on the bottom left.

So that of course would provide me with 180°.

So it's ambiguous, we're not sure about it.

We're still not sure about it, which is why we need to be really precise because we see the interior angles of say, labelling this triangle ABC would mean that it is indeed 180°, right? But if we're then just talking about the interior angles within that shape, it's offered debate, right? We don't know, it could be 180°, it could be 360° if we include these two angles down here, which coincidentally form a straight line, give us 180°.

So I'm putting my hands up in the air and saying, "We're not sure about that statement." Okay? So with that in mind, what I'd like us to consider is the following questions.

So pause the video now and have a go at the independent task.

Excellent.

Let's go through some of these answers then.

So we should be familiar with solving an equation here.

So if we're going to do this, what we get is a nice bar model here, which I've given to set you up here.

And what we get is we get 50 plus 34, which gives us, of course, 84.

So I know that this part here of my bar model represents 84.

So I need to do 180 minus 84 and what does that give me? That gives me of course, 96.

So I know this part of my bar model is going to be of course, 96 as a result.

So I can say "a" is going to be equal to 96, okay? Now I can go on from there to do "b".

So if I'm going to do "b" what would that be? Well, I can solve it like an equation linearly or I could do a bar model.

You can choose which one you want to do.

It's entirely up to you.

I'll do it just as a linear equation here and I'll do "b" plus 43, plus 19 is equal to of course, interior angles of a triangle sum to, one more moment, 180°.

Yeah, good.

So 180°.

If I add 43 and 19 together, what do I get? 62.

Very good.

So b + 62= 180.

What do I do now? I don't add 62.

I, good, subtract 62.

So I subtract 62 on both sides.

And what do I get if I do that? Well, I get a "b" of course is equal to, a hundred and, come on, eighteen.

Right, 118.

Very good.

So that's my answer, "b" is 118.

We can always check our answer, can't we? We can just do 118 there, add together 19 and 43 and I should get, of course, the interior angles of a triangle, which are, good.

180°, very good.

So moving on to "c" now, this one's a very special case.

What type of triangle's this? Shout at your screen.

What is it, what is it? Yes, very good.

It's a right angled triangle, well done.

Mr Thomas is very happy there's a result.

You know what you're talking about.

This is great.

So I can mark that as 90° and then it becomes actually quite simple from there.

I can just do 90 plus 27 and then that is going to be equal to of course, ooh, is it going to be equal to? Of course it's not.

We add "c", don't we? We add that unknown angle and that's equal to 180°.

So then what I can do is add 90 and 27 together, which of course gives me, what does it give me? 117.

So 117 plus "c" is going be equal to 180°.

So then I can subtract 117 on both sides.

And what am I left with? I'm left with on the left hand side "c" is equal to, what is it? 63, isn't it? Very good.

So "c" is equal to 63.

Now this is a very special case for "d" as well.

What's going on here? What do these dashes mean? We know what these dashes mean.

They mean the lines are equal.

So this is going to be a very special case.

This is going to be an isosceles triangle.

And I know that the angles in an isosceles triangle, the ones with base are equal, right? So that one there is going to be, it's going to be "d"? Of course not.

No, no, no, no, no, no.

The ones with base, this is going to be the same.

It's going to be 67°.

So what I need to do is I need to do d + 67 + 67 is going to be equal to 180, 'cause that's the total interior angles in a triangle.

If I do 67 plus 67, what do I get? Well, you could do 67, you know, multiplied by 2, two lots of 67 and you'd get of course 134.

So "d" plus 134 is equal to 180, And you can then on to solve it and what I get, I subtract, of course, 134 from both sides, subtract 134.

And I get, of course, what do I get if I do that? Can you tell me what it'll be? 46, very good.

So "d" is going to be equal to 46°, good.

Now "e" is a little bit stranger.

What's going on there? Well, it's the same idea, exactly same idea, but this bit here is going to be "e" as well.

So all I do is I say to 2e plus 103 is equal to, interior angles, 180°, good.

So that is going to be there.

I can then go on to solve it and I get, of course, I need to do 180, subtract 103, and then I need to divide it by 2.

And if I do that, I get 77 over 2, which of course is equal to, what is that going to be equal to if I turn it from there? I'm going to get 38.

5°, okay? And then finally, this is a very, very special case.

This is called an equilateral triangle.

So I know the angles in a, interior angles in a triangle sum to 180°.

So I know it's going to be "f" on this bit here, cause they're all equal.

All the angles are equal inside here.

So it's going to be 3f is equal to 180°, therefore divide it by 3 on both sides, divide it by 3 on both sides, there we go.

A bit wonky, it's going to be equal to 60.

And there we have it.

That's our independent task done.

Very good.

Okay, moving on then.

We want to think about this explore task, right? I've got some bar models here that represent the shape that I have just over here, right? They're all over the place, I'm not sure what's going on.

We need to think.

Is this boy correct? I think the red angle is the same size as the dark blue and green angle combined.

Do you agree? Do you disagree? Right? Have a go, complete those bar models there and think about whether you agree or disagree? Pause the video now.

Okay, sweet.

Let's go on to see.

Maybe we need some help, right? And I'm happy to provide that.

That's my job here, right? Mr.Thomas' job to help you learn and do as well as you can, right? Be rubbish otherwise.

So let's have a go at doing those bar models.

I have just split the, all I've done is I've split the shape up into a triangle here.

So I know that this of course, is a triangle.

So I know that's going to be 180°.

I'm happy with that.

I can then think, "Well, back to when we had that try now, what's going on there?" Well, all of those angles sum up to 360°, right? That is a, if I do this, this and this, that is of course in the form of a triangle, then you've also, which is of course, 180° and then you've got a straight line there.

So that gives you of course, 180.

So I know that that's the case.

I can then think, "Well, I've got this straight line, of course, right? Seeing that quite a lot." So that's going to be 180° and then I'm thinking, "Well, I've got this, I've got this and I've got this.

And that's all part of a bigger triangle, so I know it's 180°." So I'm going to leave you there to think about whether or not he is correct in saying that.

I'm not going to help you 100%.

You can explore that as time goes on, okay? I think you can do it, I think you can do it.

You have a really good idea of how we do that sort of thing.

So have a go filling out the answer now, having seen what I've done and seeing whether or not he is correct.

Pause the video now and have a go.

Excellent.

That brings us to the end of today's lesson.

I just want to say from the bottom of my heart, I think you've done an amazing job, right? If you've managed to persevere, and you've got those answers and you've had a go at that explore task, et cetera, you've done really, really well.

I'm sure you're on track to do really well as this unit progresses.

It's really important for the rest of it, that we understand that core concepts of the angles in the interior angles, in that triangle, sum to 180°, right? It's just the beginning, really important you understand that.

And if you can please take a picture of your work and ask your parents or carer to share it with your teachers so they can see all the fantastic things you've learned today.

And if you would like, you can even ask your parent or carer to send a picture of your work to @OakNational on Twitter, so I can actually see your lovely work too.

When this goes live, I really want to see loads of people drawing those triangles out, making sure, "Yeah, I've got that.

I've got that an answer, Mr. Thomas.

I'm really happy about that." Be really, really amazing if you could do that, okay? And that's it from me.

I hope you have a great day where you're learning until your heart is content, of course.

It's sign off from me and I'll see you soon.

Take care.

Bye bye.