# Lesson video

In progress...

Hello everybody.

My name is Mr Kelsall and welcome to today's lesson about revision of angle properties.

And before we start, you'll need a pen and a piece of paper and somewhere quiet that you're not going to get disturbed.

Don't forget to remove any sort of distractions for example, put your mobile phone on silent or move it away completely.

And then pause the video and when you're ready, let's begin.

Our lesson today is all about revision of angle properties.

We will start by looking at angles on a line, angles around a point and angles on a right angle.

We'll then move on to angles within a triangle and quadrilateral.

We'll then look at parallel lines and solving problems within parallel lines and all the shapes.

And after that, it's quiz time.

As I've mentioned, you'll need a pencil and a piece of paper, ideally graph paper, and the star words for today we'll be talking about vertically opposite angles, right angles, we'll be looking at triangles which are scalene, isosceles and equilateral triangles.

Will be looking at quadrilaterals, mainly parallelograms, trapeziums, a rhombus, square, rectangle and we'll be using the word parallel.

In order to access this lesson you will need some basic angle facts and I'll go through these now.

You will need to understand that angles within a right angle add up to 90 degrees.

A right angle is notated by a small square.

If I split this and I say that this angle is 40 degrees can you account the remaining angle? So you do 90 degrees take away 40 degrees gives you 50 degrees which is the missing angle.

You can use this in a variety of ways.

Sometimes you won't always see right angles which look like a right angle, but if it's notated by a square it will be a right angle.

Second factor is you need to understand angles on a straight line add up to 180 degrees.

So that means if I look at my example here I know these angles add up to 180 degrees.

So 50 and 60 is 110.

180 takeaway 110 gives you 70 degrees or you could do it 110 and carry out adding up to 180 degrees to get 70 degrees.

But angles on a straight line add up to 180 degrees.

You'll also look vertically opposite angles.

And this is all to do with angles which are also on a straight line.

If I look at this example here, I can see that I've got 50 degrees as my first angle.

I'm trying to find my second angle which is on a straight line.

I'll do 180 degrees take away 50 degrees gives me 130 degrees.

I then need to find my other measure angle here.

Well, I've got another straight line there.

So 130 degrees add on something gives me 180.

So 180 take 130 gives me 50 degrees.

So I can prove that these angles are vertically opposite by using my angles on a straight line idea.

Our final angle is 130 degrees.

The next skill is to understand angles around a point.

So if I have a singular point I understand that all these angles add up to 360 degrees.

Sometimes I might need to use more than one step.

For example, this question I can say I've got a straight line there.

So 90 degrees, add 90 degrees, it gives me 180 degrees.

So I've found one missing angle there.

That means I've just got one angle remaining to find.

Next rule is the angles inside a triangle add up to 180 degrees.

Now you will get three style questions on this.

The first one is where you get a triangle with different angles and you'll be given these angles and you're asked to find a missing angle.

The second one will be understanding properties of an equilateral triangle where all three angles are equal and all three angles are 60 degrees.

Your third type of question is where you've got an isosceles triangle and you've got two sides which are the same length and therefore two angles which are the same size.

You might be given one angle and be asked to find the other two angles, or you might be given one of the two angles and asked to find the top angle.

But either way angles within a triangle add up to 180 degrees.

And your final skill is all to do with angles within a quadrilateral.

Now, normally with these style questions you will be either given three of the angles and asked to find a fourth angle.

So if I told you that was 90 degrees, 90 degrees and 60 degrees, you'll be asked to find the missing angle here.

I need to add on another 120 to find my missing angle.

You might also get questions which ask you to use properties of the shape that you know.

So for example, this is a parallelogram and I know that opposite angles are equal size.

This is a rhombus and I know these angles are equal and these are angles are equal.

So you might be asked to use the properties of the shape that you given.

So our new learning and our first task today, you've got several questions that you can have a look and have a go on.

They are all to do with angles on a right angle, angles on a straight line, angles around a point, vertically opposite angles.

Before you do that there are three questions on the board and these are real thinking questions.

The first one says, the angles on the right angle add up to 90 degrees, prove this.

How can you prove that angles on a right angle add up to 90 degrees? The next one is angle on a straight line add up to 180 degrees.

Again, prove this, convince me, show me.

Imagine I'd never seen an angle before and I need to understand that angles on a straight line add up to 180 degrees, prove it to me.

And the same idea with 360 degrees.

Pause the video, and then when you're ready, press play to continue.

So perhaps the easiest way to prove that angles on a right angle add up to 90 degrees is by finding yourself an angle measure.

So you can fold a piece of paper.

Fold it again, it will give you a 90 degree right angle.

You can measure this on a protractor.

To prove that angles in a right angle add up to 90 degrees you can take this piece of paper, you could fold it in half and you can measure each side to prove that it add up to 90 degrees.

This is what we call your base fact.

And the reason it's your base factor is because you can use it to prove the other facts.

My second thing is to prove that angles on a straight line add up to 180 degrees.

Well, mostly much now I've got my right angle there.

If I continue this and I do another right angle that gives me a straight line.

So I've proved that angles on a straight line add up to 180 degrees.

It doesn't have to be a straight line that we normally see.

You might see a straight line but it's at an angle and I might draw it like this.

I might have a right angle and another right angle.

But I know that two right angles, 90 and 90 add up to 180 degrees.

So that line there, must be 180 degrees.

And my final point I need to prove is 360 degrees.

If I know that a straight line is 180 degrees, then I know another straight line is also 180 degrees and 180 degrees and 180 degrees is 360 degrees.

This brings us to using these facts to start by solving problems. Well, the first question asks angles in a right angle add up to 90 degrees.

I know I've got used 70 degrees of the 90 which means that this is a further 20 degrees.

question.

Question number two relies on vertical opposite angles to understand that that is 50 degrees.

You can work out by sum of that one straight line.

So this angle must be 130 degrees and this is another straight line.

So 130 add 50 is 180.

You can do with the same with the straight line at the bottom.

50 add something equals 180 must be 130 degrees.

And your final task, you're given two angles out of three possible angles.

So my three angles add up to 180 degrees.

One is 50, one is 70 together those add up to 120 degrees which means that add a further 60 degrees and that gives you 180 degrees.

So for our final two questions, the first one is looking at angles around a point.

Now I know that these lines here look like they're right angles.

And normally, if you aren't told they different you could presume they're right angles.

However, I've been told that this angle is 85 degrees.

So that means I can't presume that either of these are right angles.

So I need to use my angles on straight line properties to find out this missing angle.

85 degrees and something equals 180 degrees.

I can think, well, I'm going to start with my 180 degrees.

I'll take away 80 to give me 100 and I'll take away another five which means that this missing angle is 95 degrees.

Now, I've got some information.

I've got three angles out of four angles.

I know all four angles add up to 360 degrees.

So I need to find out what these three angles add up to.

I'm going to add on the 95.

To do that I'll add on 100 and take away 5.

So that's 235 take away 5 that's, 230.

And then going to add on 85.

So 230, when I add on 100, which is 330 and I'll take away 15, which is 315 degrees.

So I know that these three angles add up to 315 degrees.

So all that's left for me to do is say, well I need to find the difference between 360 degrees and 350 degrees.

You can count from 315, add 5 is 320, add 40 gives you 360.

Or you could use a written method.

You could say 360 take away 315.

So 10 take five is five.

Five take one is four, three take three is zero.

So this missing angle is 45 degrees.

And my final one involves a little bit of thinking and I need to use a few different angle properties.

The starting point for me is that I have a right angle here and it's been split into three equal parts.

So 90 degrees divided by three gives me 30 degrees.

So I know this angle, this angle and this angle are 30 degrees each.

Oh, I only need some bar angle is 30 degrees.

And I need to find out what this missing angle here is.

I know angles around the point add up to 360 degrees.

And I know that I've used 30 degrees of this, which means that that big angle the reflex angle is 330 degrees.

And that brings us to the develop learning for today.

So here we have two tasks and then several questions.

Task Number one, look at the angles in the triangle, they add up to 180 degrees.

Can you approve this? Same with angles in a quadrilateral they add up to 360 degrees.

Can you approve this too? Once you've done that, have a go at the questions on the screen.

Pause the video and press play when you're ready to continue.

So I'm trying to prove that triangle has angles which add up to 180 degrees.

So I have my triangle here and if I rip off this corner and put it here.

If I rip off this corner and rotate it and put it here and then if I rip off this corner, turn it around and put it there.

What I can see is all three of these angles combined make a straight line.

Now I know the angles on a straight line add up to 180 degrees, therefore angles inside a triangle must add up to 180 degrees.

I can apply a similar knowledge to angles inside of quadrilateral.

If I take myself a quadrilateral, I start from any vertex and I join a vertex to all the other vertices.

I can see that I create two triangles.

Now I know one triangle has angles of 180 degrees, and I know the other one has angles of adding up to 180 degrees.

Therefore, I know the angles inside this quadrilateral must add up to 360 degrees.

And I can repeat this with a range of different quadrilaterals.

So if I try a trapezium, I choose a corner and I join up that corner to all the other corners, I create two triangles.

I can do the same thing.

I even choose unusual shapes that we don't normally think of when we looking at quadrilaterals.

And I'm going vertically one vertex to the vertices, I create two triangles.

Therefore I prove that angles inside a quadrilateral add up to 360 degrees.

The next we need to look at these style of questions.

Now my first question, I'm given two angles and I need to find the third angle.

50 degrees add 30 degrees is 80 degrees.

So my third and missing angle must be 100 degrees.

Be careful of this, because these triangles deliberately drawn incorrectly.

Because I know that this angle is less than a right angle so it should be an acute angle.

So it should be less than 90 degrees but actually using the other numbers, it comes out as 100 degrees.

Be aware of things like this.

My second triangle is the green one and I can see that these lines here tell me all three sides of equal length.

If all three sides are equal length, all three angles are equal size.

So I'm thinking 180, split it between the three angles.

I can do this mentally because I can do 18 divided by three is six, therefore 180 divided by three is 60.

So each one of these angles is 60 degrees.

And finally, my third triangle is an isosceles triangle.

I know that it has two base angles that are equal and I've been given one angle which is 50 degrees.

180 degrees take away 50 degrees, I can do 18 take five is 13.

So 180 take 50 is 130.

So I know that these two angles add up to 130 degrees.

Therefore all I need to do is split 130 degrees by two.

You could do it mentally and do 13 divided by two is 6.

5.

Therefore 130 divided by two is 65.

Or you could use a written method like I'm going to use here.

How many twos go into one, zero carry the one.

How many twos going to 13, six, it's one leftover.

How many twos into 10, five.

You can solve it whichever way you choose but each of these angles is 65 degrees.

Then we get to some more complicated triangles but I can still use the properties of the triangles that I know.

If I start, I know I have each of these are 60 degree angles.

I know I've been given a 40 degree angle there and I know angles around the point here, add up to 360 degrees.

I'm just going to draw this bit here.

So I've been given 60, 40, that adds up to 100 degrees.

Therefore, my remaining two angles must add up to 260 degrees.

Because 100 degrees add to 260 degrees is 360 degrees.

Therefore if I divide 260 by two, I'll find that each of these angles is 130 degrees.

I then need to come back and consider my base angles here.

I know my top angle is 40 degrees.

So 180, take 40 leaves 140, then split in 140 by two.

I could split 14 by two is seven.

So 140 by two is 70.

So each of these angles is 70 degrees.

Now leaves me my final angle.

Now my starting point here is that I know from 12 to 3 o'clock I form a right angle.

The next thing I know is this right angle has been split equally into one, two, three parts.

Therefore 90 degrees divided by three is 30 degrees.

So this angle here must be 30 degrees.

It's going to clean the screen.

If I know this angle is 30 degrees, I need to account this angle.

Well, 360 takeaway 30 is 330.

So this reflex angle here must be 330 degrees.

And I also be asked, what are these angles here? Well, I know this is an isosceles triangle because the distance from the centre to one is the same size as the distance between the centre to two.

So 180 degrees take away 30 degrees leaves me 150 degrees.

150 divided by two means that these angles are both 75 degrees.

Now it brings us to our independent task for today.

Before we start this question I have to tell you that all the questions so far involve you really using all the angle laws that you have so far and really thinking through what you know as well as what you don't know.

This question is exactly the same.

It uses all the properties we've discussed throughout the lesson, though you have to really think them through to understand which angles are which and how you can find the missing angles.

Pause the video and when you're ready, press play to continue.

My starting point is this angle here.

I know it's a right angle.

I know if I split it between one and two, I know that each of these degrees so from 12 to 1 is 30 degrees.

From 1 to 2, 30 degrees, 2 to 3, 30 degrees.

This angle here is 30 degrees.

Next thing I know this angle covers two hours.

It goes from 10 to 11, 11 to 12.

So I know that must be 60 degrees.

I could use the properties of angles on a straight line to find out this angle, and I know I've used 60 degrees of my 180 degrees so this must be 120 degrees.

And now I have a right angle here and a right angle here.

In fact, I'm going to add in all my right angles cause that will help me.

You'll notice there's quite a lot of right angles.

Okay so that eliminates a lot of angles we need to find.

I'm now going to to look at this angle.

If you look closely, this forms a quadrilateral, it's actually a trapezium, isn't it? Because I've got one pair of parallel sides and I know I've got an angle of 90 degrees, 90 degrees which is 180 and then a further 120 degrees which if I add 20 gives me 200 and 100 gives me 300.

So that means this missing angle must be 60 degrees.

I'm now going to move on to the triangle in the corner here.

Now I've got one, two angles left to find.

I'm going to clear this and show you how I found these angles.

You remember parallel lines.

If you have a line dissecting them, you find out this angle, I also have this angle, this angle and this angle.

Oh, have a look here.

I have parallel lines and if I extend this line, if I know this angle I can find out this angle and this angle, I can extend this a bit more, this angle too.

Perhaps I know that this angle is 30 degrees because I know that from between 12 to one o'clock is 30 degrees.

Therefore this must be 30 degrees, 30 degrees, 30 degrees.

If I go back to this triangle, I've got a 30 degree angle, a 90 degree angle, which takes me 120 degrees.

That means this final missing angle here must be 60 degrees.

I was going to say, you might have found this differently.

You might have said that from one o'clock to three o'clock covers two gaps.

So that is 60 degrees.

Then you've got your 90 degrees, 60 degrees and 90 degrees is 150, which means that is 30 degrees.

There are a range of ways that you can solve the missing angles but it's just a thought process of understanding what rules you can apply to this problem.