Lesson video

Hello and welcome to this lesson about angles, partitioning angles.

Please take a moment as always to clear away any distractions, be that your brother, your sister, or pet, and find a quiet place where you're not going to be disturbed.

Remember, if you're watching on a computer or a desktop with only description or laptop, make sure that you've got your phone silenced like I do.

Right, all those app notifications turned off, particularly if you're watching via your phone as well, really important tablet, et cetera, anything that could hang up and disturb you, please make sure it's silenced.

And with that, let's get started.

So have a go at the Try this then.

Find all the factors of 360 for me, and then use the information below to sketch similar diagrams for a selection of the factor pairs.

So we can see that I can visualise the fact that 90 and 40 are factors of 360 using this drawing.

I'm going to let you think about that for a moment and pause the video, have a go at that now.

Okay, fantastic, let's go through with them.

So what I think is really important here is that there are so many different options for the factors of 360.

Remember a factor is something that you can divide something perfectly by, and there are no remainders, really key.

There's no remainder when you divide it.

So these are all the different options you could have.

One, two, three, four, five, six, eight, nine, 10, 12, 15, 18, 20, 24, 30, 40, 45, 60, 72, 90, 120, 180 360.

Whoo, I did that in one breath.

Okay, so all of those answers are acceptable.

There was so many that you can have, and the key bit being here for that part B is that if you sketch that out, you get that's a 90 degree angle, 90 degree, 90 degrees, 90 degrees.

So we have four lots of 90 degrees.

Well, what do I have for this one here? I've got this marked angle, this marked angle, and this marked angles, that's 120 degrees, 120 degrees, 120 degrees.

How'd I work that out so quickly.

Well, what I did was at a 360 divided by three of course.

So I've got three lots of 120.

Do you think that I've done over here? What have I done here? I've got how many marked angles, one, two, three, four, five, six.

So I've got six lots of what would it be to get me to 360, three times what.

60 degrees, right, so six lots of that one.

So we can kind of take off like some of these that we've marked on.

We've done three, we've done four, we've done six, and we've also done 120 of course, by definition with the three matches that went up and then the 90, of course, and then the 60.

So we've done a few of those already.

You may have done a few more involving these, which is fantastic.

I'm really happy if you managed to do that.

Very good.

Let's continue then.

So we've got this connect task, which you're going to think about now, which is, I want to think about the equations we can form from those given angles.

Now, we know the angles in a straight line, sum to what? 180 degrees, right? So I can think of an equation I can form here.

Now, there are two different options.

You can just go over a normal algebraic approach or we can use what we call a bar model.

Now you may have encountered that in primary school, a lot of primary schools are starting to do that nowadays.

Which is fantastic.

So if we were to use a bar model, we can say, that of course we know that a is smaller.

So we want to make sure that my bar is going to be slightly smaller so I've got a and b here, and I can say that is going to be equal to what did we say? 180 degrees.

So, I can say that that's going to be 180 like that, or I could simply say a plus b is equal to 180 from that I can derive quite a lot of things.

I can say that, of course, 180 subtract b would give me a, so 180 minus b would give me a, I can also say that b would be equal to 180 minus a.

So there are so many different things you can tell from that information.

It's quite powerful, how much you can tell just from that alone.

Have a think about this diagram.

Angles around a point, what does that sum to? We said that at the end of the last video.

What was that? Angles around a point sum to? What was it? Can you remember? What was it? 360 degrees, right? So, a plus b is equal to, in this case 360 degrees, we can then do exactly the same as we did over here.

We can say that a is equal to 360 minus b, and then we can do b is equal to 360 minus a.

You can also do that bar model to represent it, if you want to.

We know in this case a of smallness onto that small chunk, my bar for a and then b here and then I'm going to have a nice spread out one here which would give me 360.

What about this one over here? Well, slightly stranger.

We've got a plus b of course, but then what do we realise over here? We've got 90 degrees.

That's a right angle.

So plus 90 is equal to 360.

I can say, well, of course a plus b first subtract 90 on both sides.

I get, what do I get if I do 360 minus 90.

What would that give me? 270, right? It's 270 and then rearrange it like so, with 270 minus a gives me b and then 270 minus b gives me a, so there's all sorts of different options that we can have there, really, really powerful.

What about the inequalities though? So inequalities, well, what is inequality? You may have come across that before it's involving greater than, and less than, or it could be greater than or equal to, or less than or equal to.

So using those signs, just there, how can we think about what we can do just here? Well, this one, we can clearly see that there's an angle carved out here.

We don't know what it is, right.

So what I can think about here is a plus b must be less than, less than 180, right? So then I can do, as I did before, I can say well, a is less than 180 minus B, et cetera, et cetera, et cetera, you treat it as if it was an equal sum.

You can still do that, I'm saying, so the algebraic manipulation there.

What about a few of these then over here? Well, we can say that a plus b in this case is going to be less than the sum marked bit here that we don't know.

So we can say that's going to be less than 360 degrees.

Yeah, what else can we say? Well, we can say that 360 minus B for that part there.

What would that read? If I was to read that out, what would that read as? A is less than 360 minus b.

Right? And then finally, we can say that b is going to be less than 360 minus a.

Yeah.

So we've got all sorts of things just there.

What about that final one then what's going on there? I could say a few things about that.

I could say that b is less than 180.

Yeah.

That seems reasonable.

I can say that a is very clearly.

I can say a is very clearly.

I can see that a is very clearly less than 90 there.

Right? So there is all sorts of things you can do.

And you may even yourself be able to combine something that may merge the two together.

I'll let you have a think about that one.

Now what I'd like you to have a go now is your independent tasks.

So fill in those blanks.

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

Pause the video now and have a go.

Awesome.

Let's go through it then.

I'm going to take you've done that.

So the answers are as follows.

If a known blank is split into different parts.

So, what's the topic we've been analysing today? Well, of course it's angles, right? So if a known angle is split into different parts, so we can fill that as angle, tick that off, split into different parts.

We can form a blank.

We can form equations, right? This is all to do of Algebra forming equations.

For example, if a 90 degree angle, well, that's a coincidence, we've got a 90 degree angle over here, haven't we? Looks like a 90 degree angle split into two blank angles of a and b.

We can say that well, angles a and b, they are acute.

They're smaller than 90 degrees.

So acute angles of size a and b, we can say that blank plus blank equals blank or 90 minus blank is equal to blank or 90 minus blank is equal to blank.

Sounds so weird saying blank all the time, isn't it? So if I add those two angles together, what do I get? Well, a plus b will have to equal 90 degrees.

Wouldn't it? So I can take an a, a b off 90.

So I know if I do 90 minus a, well, the whole thing.

So pract a would give me B so I can do that there.

And then I can say 90 minus B in this instance would give me a, so we can take those off and we know we're done and we're right.

We've got it right.

Very happy.

This is always very, very good.

Let's continue.

So you've got an explore task now, and I'd like you to think about this.

Can you form two equations using two different angle facts to solve for a, pause the video now, if you'd like to have a go, or if you'd like to stay on and get support or go through the answer by all means, let's continue.

Excellent.

Let's go through it then.

So you can form two equations using two different angle facts to solve for eight.

Well, if we think about this, this of course is a right angle here.

It's a square we've got right angles and squares, right? So I could say on the first instance, a plus a plus 90 is equal to, well, if we notice that is a point, of course, there's some around a point, so it's going to be 360, right.

And subtract 90 on both sides to just balance it out.

And I get, of course, a plus a is equal to 270.

I can then say, well, two a would equal 270 and then divide by two divide by two.

And that gives me, of course a is equal to 135.

So I know I've got one answer there.

Did you get another answer? How did you get a, is equal to 135 if you're using a different method? Well, what we can think about here is we could say that we've got, if we use my rubber.

Because I know that this is going to be 90, I could split it down here.

And I could actually say that that is 45 degrees just there.

And that is a, and that's a straight line.

So what I've done is I've bisected the end work, split it in half, right? So what I can say there is that a plus 45 is equal to 180, and that's a really nice one to solve.

I just subtract 45 or do the inverse on both sides.

And that gives me, of course a is equal to 135.

So I've sold using two different methods there for a, I've got 135 in both those instances there, which is amazing.

I'm really happy with that.

So that brings us to the end of this lesson.

So, so critical what you've learned today.

Partitioning angles and solving them, really, really good.

So we're going to learn more about that as time goes on.

I hope to see you in the next episode, make sure that you do that exit question.

You can check your learning and make sure you can show to everyone how well you've done.

Really, really good that you can do that.

So take care in the meanwhile and I'll see you soon.

Bye bye.