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Hello, and welcome to this lesson on Angles, Finding Unknown Angles.

This is a really, really important lesson.

I know I say that so frequently, Mr. Thomas, you keep rattling on about how important these lessons are, it's 'cause they always are.

They're always so important that you learn this, right, but this one really comes up in exams a lot and fundamentally, it's so important you know this.

So, what I'm going to ask as always is that you remove any distractions that could be distracting you so for example, it could be your brother, your sister, or your pet, and you find the quiet place where you're going to settle down, you're going to be able to concentrate on the powerful maths we're about to do.

So without further ado, let's get started.

So have a go at the Try this.

Got a student that is saying, which of the sectors could you use to make a semi circle or a circle? So, think about which ones you can combine together to make a semi circle or a circle.

Think about the amount of degrees that are required for each.

Pause the video, have a go now.

Okay, I'm assuming you've un-paused the video and you're ready to go on.

So, this is what I've got in terms of my answers for this.

If you think about a semicircle, the way you can create that is with the 105 degree angle over here plus the 75 degree angle, and that gives you 180.

So, well done if you've got that market, right? If you've got 60 plus 45 plus 75 degrees, that would give you 180 as well if you combined three of them.

So that one, that one that, and where's the 75, down there, good.

Or you could have that one as well, is two sixties.

So, if you, for the circle, if you sum all the animals together, you get 435, which is 75 degrees over what you want.

So, that doesn't work unfortunately, but what does work is if you do 105 plus 60 plus 60 plus 45 plus 90, that gives you 360.

So that works, that's really good.

If you've got that, absolutely brilliant! Give yourself a big tick, you got it right, very good! Let's move on then.

So, we're going to learn something quite interesting today.

We're going to think, well, what equations can we form from this bar model, right? If you're feeling confident for this, pause the video now cause I think you may have encountered this before.

If you're not too confident, stay listening.

So, what equations can we form? Well, what we can tell is the whole bar is worth 200, but we can see that this portion is worth 150 and this portion is worth a.

So what we can say is that 200 is equal to 150 plus a.

Now we can derive loads of information from that.

We can say, of course, that 200 subtract a is equal to 150 because we can see that chunk is eight so if I did 200 minus that, I'd get 150.

I can also say that 200 minus 150 would give me a, and that can simplify, can't it? What could that simplify to? 200 minus 150 is? She'd get that? 50, right? So, 50 is equal to a.

There's loads of things that bar model is so powerful it's a very, very short amount of information, but actually it can say so much about what we're doing and actually we could go into negative, we've got all sorts of realms, but those are probably the most interesting ones we can consider.

So those, the more formalised version of what I've got that.

Okay, I've got another Connect task there.

So, I want us to consider why do the following bar models work with these shapes? Now, I've got 90 here because this whole thing is a right angle, right? That is worth 90 degrees and I've got a here, right, and I've also got a there, 'cause those angles are equal and that is clearly 45 degrees there.

So I can say that a plus a plus 45 gives me 90.

So that provides a reason for that one there.

I can also see all of these are equal here, a, a, a, and a.

Now you see there's a double dash there that's different to a there.

That basically says that that angle that is different to the a that I have in the previous question.

So, I can see that I've got five lots of a there.

I've got one, two, three, four, five, lots of a there and it sums to 360.

Can you remember why? Why does it sum to 360? Mr. Thomas has got the answer! What is it? It's angles around a point sum to 360 degrees, right? So I've got that bit there which is brilliant.

I've then got this final piece of information.

We can see that is a what sort of line? It's a straight line, right? And angles and a straight line sum to? Yeah, you got it! 180 degrees, very good.

So, that one there gives us a reason of that being a 180.

It's a plus 150 gives me 180.

So I can clearly see how that all connected together.

They look so beautiful.

I love bar models.

They look so amazing when they produce like that.

There's so much information, it's so easy to sell the equation to deal with it.

I'll leave my love of bar models for another time but you get the idea.

Now, you've got an independent task I'd like you to complete here.

So, I want you to fit in the blanks for that there.

You may want to go back in the video if you need some help.

So, pause the video now and have a go at that task for me, please.

Okay, I'm going to assume you've got the answers down and you're ready to mark your work.

So let's go through this.

Now, it says, here we can use blank, blank to form an blank.

We can then blank this equation by using useful related equations.

Now, I don't know what you got there, but that's, there's quite a lot of things going on there.

So we can use blank, blank what can we use to form blank? Well, I think it might be easier to do this to form an, using basic grammar, we can conclude that it's going to start with a vowel because it's got an there.

So that one is definitely going to be an equation.

So let's start with that.

What can we use to form an equation? Is it going to be any of these over here? Well, it's not.

We're not talking about variables in any way or terms at all or numbers.

So, we can use it then seems to be angle facts, right? They seem to be paired together, that seems clever.

So if I use that angle facts to form an equation, that makes a lot of sense.

Do I need to use angle facts over here though too? Oh I'm not sure.

We can then blank this equation by using useful relates to equations, right, so we can then solve this equation.

That makes a lot of sense.

So, I've used up those ones there and I've now got numbers and letters.

That's brilliant! I'm happy with that, it seems good.

So, for example, in the image above, but we can see that 360 is equal to, well, this one here is the 360.

What is that equal to? Something add something.

Well, I've got c and c, so I get two lots of c.

So I can use that two c there plus what else? 90, isn't it.

So plus 90 degrees.

Now, therefore something is equal to something and therefore c is equal to something.

So, well, what I can see is, well, two c again needs to be used maybe we should have had another two c involved in there.

Maybe that's slightly misleading.

Two c is equal to 270 and therefore c is equal to 135.

So, I'm hoping you may have got that.

Just there was a slight trick there that you didn't have two c repeated, but I hope you saw that that was going to be two c.

So, if you didn't get that, that's unfortunate, but hopefully you saw the little trick there.

Okay, got to make things a little bit hard every now and then.

Brilliant, let's move on then.

So you've got an Explore task now.

Now this is really, really clever, some of these, and I want you to really think about these.

Think about what we've learned about creating patterns, thinking about what we know so far to do with angles.

What can we say about each of those angles there? Pause the video, have a go at that question now.

Hi everyone.

My name is Ms. Jones and I'm just going to take you through some extra support on that question.

So, if you've already completed it and want to hear the answers, that's great! If you're not sure, and you want some support, we can do that now.

Okay, so let's look at this together.

We knew that we had some regular hexagons and squares and we needed to find the missing values, a, b and c.

Okay, let's look at this first one and think about what we know already that can support us to find a.

While I can see here that these shapes are or regular, which means that all of the internal angles in this shape are the same size.

Okay, so if this is a, I know that this will be a, this will be a, this will be a, okay? So, I can put in that this is a, and this is a, and what we have here are three equal angles around a whole turn.

And I know that what I can do here is take 360 degrees and divide by three to find the value of a.

So if I do that, 360 divided by three, what do I get? I get 120.

So, what I found out is that one of my internal angles in a regular hexagon is 120 degrees.

Now, I can use that to help me with some of these questions as well, cause these are also regular hexagons.

So, all my internal angles within the hexagon will be 120 degrees as well.

So what do I already know here? Well, I know this is a square, so this has to be 90 degrees.

I do not know this value, but I do know that this is also a, 120, and this one is also 120.

So we're getting now we know enough information in order to take our facts of 360 degrees and this time, because we've got unequal parts, We can subtract what we have already.

So let's take 360 and let's subtract 120 and then another 120 and hopefully, that will give us this half and then we need to subtract 90 and that should equal two b.

Okay, so 360 take away, that's could be scabbard 240 will leave us with 120, take away 90, will leave us with 30.

So I know that two b is equal to 30.

I'm not finished yet 'cause that's two b.

We need to find out what b is.

What's the last thing I need to do? I need to divide by two.

So b should be equal to 15 degrees.

Okay and let's look at this final one here, three c.

Again, think about what we already know.

We know the whole turn would get us 360 and we know that this is a right angle of 90 degrees here, we know that this is a right angle, we know that this whole angle, within our internal angle of a hexagon here will be 120.

So, all we need to do here is take 120 and subtract 90 to find three c.

Let's worked out up here.

120 subtract 90 degrees, it's going to leave us with 30 degrees.

That gives us three c.

So, if I want to find out what one c is equal to, I can divide by three and c is equal to 10 degrees, okay? Hope you did okay with that.

Do you not worry if you needed a little bit of my help there.

Hopefully you can see that there now and you've had to go yourself.

If you had to go, the answer's already any you're correct, absolutely amazing work! But if you do need to correct anything use the information on the screen now.

Okay, I'm going to hand you back over to your teacher once you've done that to finish off the lesson.

Thanks guys.

So that brings us to the end of the lesson.

I just want to say you've done an amazing job that you've managed to keep up as I always do, because it's so impressive if you can do that.

Such a form of like fundamental idea of maths, being able to solve those equations, especially when you've got shapes involved in all sorts of things, darting all over the place and loads of information to compete, especially if that last explore task.

Amazing if you kept up! So, don't forget as well to do that exit quiz so you can smash your learning.

You can show just how much you've learned to your teachers, to a whole load community, everyone involved.

They're amazing if you could do that, smash that exit quiz and get five out of five.

And as always, stay safe and I look forward to seeing you in the next video.

Take care, bye-bye.