Calculating angles on a line or around a point
Source of all images : Mr Kelsall or Oak National Academy

What is the size of the missing angle?

How is this drawing incorrectly drawn?

What angle would 4pm show?

Calculating angles on a line or around a point

﻿Hello everybody. My name is Mr. Castle and welcome to today's lesson about angles within a shape. Now before you start, we will need a pen and a piece of graph paper. Also, please try and find a quiet place so that you won't be disturbed. And don't forget to remove any sort of distractions. Perhaps put your mobile phone on silence or move it away completely. Pause the video and then when you're ready, let's begin. Today's lesson is about calculating angles within in a shape. And we're mainly talking about triangles. Now in order to understand this, we need to look at what types of triangles are there, we need to look at what angles within a triangle add up to. And then finally, we need to look at multi step angles if we've got an angle with a triangle, and then another step on top of that. After that is Quiz time. You will need a pencil and ideally a piece of graph paper And now new words for today we're looking at vertically opposite angles. We'll talk about three types of triangles, a scalene triangle, Isosceles triangle and Equilateral triangle. But in order to access this lesson, you need to remember a couple of facts and begin to use these facts. So Fact number one, you need to know that a right angle is 90 degrees, you need to know a straight line add to 180 degrees or angles on a straight line add up to 180 degrees. And you also need to know that the angles around a point add up to 360 degrees. You don't need to remember that vertically opposite angles are equal. Actually, this isn't true at all. You don't need to remember all those facts. If you can remember one fact you can understand all of these facts. Let me explain what I mean. If you remember that right angle is 90 degrees, you automatically know angles on a straight line add up to 180 degrees. You then know that angles around a point add up to 360 degrees. So you can use this information to start solving problems. You can work on angles on a straight line add up to 180 degrees. You can work out angles around a point add up to 360 degrees. And the same goes with vertically opposite angles. If you break it down into the steps, there's one angle which is 180 degrees. So the first part is 50 degrees. The second part is 130 degrees. You can carry that on. The first part is 130 degrees, second part is 50 degrees. This is why we call them vertically opposite, 130, 130. So actually, you could remember all four of these facts or if you just remember the first one, you can then use this to understand the other facts as we go along. Okay, so to start us off with, we're going to start looking at shapes. What shapes can you see within this picture? Pause the video and when you're ready, press play to continue. Okay, I've spotted a few, I've spotted some triangles. I've spotted some quadrilaterals, four sided shapes. One, two, three, four. Some more quadrilaterals. Then did anyone spot a Pentagon? I've got one Pentagon here, five sided shape. One, two, three, four, five. Okay, now the viewers got knowledge. Let's start with our new learning for today. We're looking at angles within a triangle. And you need to understand there are three types of triangle. You need to understand that an Equilateral triangle is a triangle with three sides and three equal angles. Sorry, I'll say that again. Three equal sides and three equal angles. And that makes sense because Equilateral has equal sides. And Isosceles triangle has two equal sides and two equal angles. And a Scalene triangle has three different sides and three different angles. So let's look in a bit more detail. This is Equilateral triangle. Equilateral triangles have three equal sides and three equal angles. Have a look at this little notation here. You'll see that if a line is drawn on one side, it indicates that all three of these sides are the same length. Another common way you'll see is three angles which shows that these three angles are equal. Also be aware of how you might see Equilateral triangles, you might see them represented in what looks like almost a square, or you might see it reflected like this one next to each other. The next type of triangle is an Isosceles triangle. These have two equal sides and two equal angles. Again, look at how it's notated here and look at the base angles here. Bear in mind, this one is an Isosceles triangle because these two angles are equal, and these two sides are equal length. And finally, we have Scalene triangles, especially because they have three different length sides, and three different sized angles. So if I look at this, I can see this angle is different, different, different, and the length of the side is different. That's much longer. That's much shorter. It's definitely a Scalene triangle. So carry on with our new learning. What triangles Can you find within this clock? Pause video. When you're ready, press play to continue I've spotted, I found a triangle. But I'm interested to know what type of the triangle is this. I know the distance between one on the centre is exactly the same distance between two on the centre. That means that this is two equal sides. And the line at the bottom ensures that both of those angles are equal. So I know that this is an Isosceles triangle. this triangle And I've tried to look at what type of triangle it was. This time instead of measuring the distance in the number and the centre, I counted around one, two, three, four and this is one, two, three, four. So I know these two sides are equal and one, two, three, four. So this side must be equal too. I've got three equal sides, and therefore three equal angles. This is an Equilateral triangle. My third triangle. Well, I'm going to measure the sides not by using a ruler, but just by counting how many gaps in between has got a gap of one, two, three, four gaps and one, two, three, four, five, six, seven gaps. So I know this is got is triangle with three different length sides. So three different length sides means that this is a Scalene triangle. So I know I've got different types of triangles. I now I need to think about what the angles in a triangle add up to. I need to know a couple of facts before this. Just to recap, the right angle is 90 degrees, angles on a straight line add up to 180 degrees because there's two right angles together, angles around a point add up to 360 degrees because we've got four right angles together. Now I'm going to tell you the angles in a triangle add up to 180 degrees. I'm going to show you in a moment, but if you want to do this dress off a triangle, any triangle. You can either get a piece of paper and take the corner of a piece of paper, and you need to colour in the three corners of the triangle, and then rip them off and move them around a book together. I'll show you how. So in front of me, I have a triangle and I've got three corners, different colours. I'm going to rip each corner and I'm going to place them on a line. Bear in mind we know the angles on a straight line add up to 180 degrees. And if you can see there as I've put all three corners down, I can see I've got a line which is 180 degrees. This proves to me I've got angles in triangle add up to 180 degrees. Doesn't matter what triangle I did it with. If I have a different triangle, I can repeat exactly the same exercise. Same again, those three angles add up to 180 degrees. Okay, now we've proved that angles in a triangle add up to 180 degrees. We need to start using this information. So here I have a triangle. In this triangle, I have one, two, three angles. I'm not interested in this angle at the moment, because this angle is outside of the triangle. Now I know that angles inside the triangle add up to 180 degrees. I've got 50 degrees, I've got 80 degrees, that's 130 degrees. So this remaining angle must be 50 degrees. If you'd like to check it, draw yourself a triangle. Do 50 degrees, do 80 degrees, and you'll see that the final angle is also 50 degrees. Okay, I've still got one missing angle here. And that's the angle here. Actually, I know that this angle is on a straight line. Let's just imagine we forgot all about this for the moment and I'm left with a straight line. I know angles on a straight line add up to 180 degrees. I've been told that this angle is 80 degrees. Therefore this angle here must be a 100 degrees. You'll see it this way. We sort of move into two step questions. Because we need to separate. I've got one triangle here, and we've got a straight line here. So you've got to use the information that you're learning now. Okay, this time you've been given a triangle, and you haven't been told what any of the angles are. So how can you work it out? Pause the video, take a few moments have think about it. Okay, so this triangle tells us that we have three equal sides because those lines tell us that each length is an equal size. So if there's three equal length sides, we know it's an Equilateral triangle. So let's use that information to help us. I know that angles in a triangle add up to 180 degrees. And I know that this triangle is made up of three equal parts. So what is each part worth? I know 18 divided by three is six. So I know 180 divided by three is 60. So each of these angles is 60 degrees. We know angles in a triangle add up to 180 degrees. I've now got an Isosceles triangle, and I need to find the missing angle. Well, Isosceles triangle have two equal angles and I know if this is 40 degrees, this angle must also be 40 degrees. I've got one which is 40, another which is 40. So that's 80 degrees. So what do I need to add to get to 180 degrees? I add 100. That takes me to 180 degrees. So I can still work out missing angles on isosceles triangles. However, take a look at this isosceles triangle. This time, we know the top angle, but we don't know the two base angles. But I do know that these two angles are equal. Well, let's start with information we know. I know angles in triangle add up to 180 degrees. And I've used 40 of these degrees. So 180 degrees take away 40 leaves me 140 degrees. Now I know that I've got to split 140 degrees between these two base angles because they're equal. If I split 14 is seven. So if a split 140 I know each angle is 70 degrees. And that brings us to our develop learning for today. So, let's have a look at these angles. There are all types of triangles and the type of triangle will help you solve what the missing angle is. Take a moment to pause the video and just see if you can work out some of the angles. And then when you're ready, let's press play, press play and continue. Okay, triangle number one. I've actually made a mistake, I should have added two lines there because that tells us isosceles triangle. Now, if I notice isosceles I know one angle is 50, and the other base angle is 50 degrees. That means I can find this missing angle and this missing angle here. So 50 and 50 is 100. Angles in a triangle add up to 180. So I know this part here adds up to 180. So I need to add a further 80 to make 180 degrees. I also need to find this missing angle. Well, I know I've used 50 degrees of my 180 degrees because this is an angle on a straight line. I'm going to count from 50, 60, 70, 80, so add another 30 to get to 80 then add 100 to get to 180. So I know this missing angle here is 130. Question number two. These lines tell us that I have an equilateral triangle. I could work out the angles, but actually I remember each angle is 60 degrees. So I've found some of the missing angles already. I now need to find out what this missing angle here is. And I know that this is an angle on a straight line. I have used 60 degrees, how many more do I need to get to 180? 60 add 20 is 80 add 100 is 180. So I know this is 120 degrees. Okay, finally we come to a little bit of a tricky one. Again, I know that these are equilateral triangles, so I know each of the angles that I'm ticking is 60 degrees. I know that because I've got one triangle, and each angle is 60 degrees. And I've got one triangle where each angle is 60 degrees. Well, let me write some of this. If this one is 60 degrees, I know that I then have a straight line here. Make it a little bit clearer, that much straighter line. I've used 60 degrees of my 180 degrees. I need to add another 120 degrees. And it's the same on this side. You could work out that 60 degrees and you could calculate that's 120 degrees or you could recognise that we have vertically opposite angles here. So this one and this one are 120 degrees. Now it's time for your independent task. So two facts you need to remember, a triangle, angles inside a triangle, add up to 180 degrees and angles on a straight line, also add up to 180 degrees. Now, can you find all the missing angles? Try and think about how you know. Pause the video. And when you're ready, press play. I know that my equilateral triangle has angles of 60 degrees. Therefore I know that angles on a straight line add up to 180. So this must be 120 degrees. In my scalene triangle here, I've got 50 degrees and 80 degrees is 130 degrees. I need to add another 50 to get 180. And actually I said this is a scalene triangle but now I've noticed that 50 and 50, adds up to 100. And they're equal angles. So actually must be an isosceles triangle. Okay, and then looking at my other angle, and I've got 80, add something gets to 180. that must be 100. And finally, I have an isosceles triangle. A little trick here. I describe this as an isosceles triangle, but this angle is 60 degrees. The other angles must also be 60 degrees. So although it's labelled as isosceles triangle, I actually know it's an equilateral triangle. And these angles here are also equilateral triangle. So they're also 60 degrees. And then even though this is represented as a straight line, I know that it's still going to be a straight line, because this angle is actually 60 degrees. That's a straight line. 60 degrees add something must be 180 degrees. So this angle must be 120 degrees. And therefore this angle must be 120 degrees. And finally, if I look at isosceles triangle, we know that actually what is this angle here? Let's use some information I know. I've got a right angle. And I've got about two parts, three parts. I know right angle is 90 degrees. And I'm splitting that 90 degrees into three parts. Nine divided by three is three. So 90 divided by three is 30. So this angle, the bottom here is 30 degrees. Now I know is isosceles triangle. So I'm doing 180 take away my 30 degrees is 150. And I Know that these two angles here must add up to 150 degrees. So if I split 150 into two, I know each angle is 75 degrees. And for my final angle using the information I know, I know this is a right angle 90 degrees. I also know it's isosceles triangle. So these angles are equal. 180 take away my 90 degrees. There's my 90 degrees. 90 degrees split between two angles, each of these must be 45 degrees. Now before I carry on, I just want to say if you've managed to get all of the correct, thumps up, absolutely fantastic, because there's a real depth of learning. There's a lot of thinking and a lot of things you need to be aware of. Congratulations on completing your task. If you'd like to please ask your parents or carer to share your work on Twitter tagging @OakNational and also hashtag #LearnwithOak.

Triangles, angles within triangles and multi step problems
Source of all images : Mr Kelsall or Oak National Academy

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Calculating angles within a shape 1: triangles

In this lesson, we will learn about different types of triangle and how to calculate angles within a triangle.

Maths

Y5 Maths

Key Stage 2

Year 5

Calculating angles within a shape 1

Angles

Geometry

THEME

UNIT

Understanding angles

Recognise right angles

Recognise acute and obtuse angles

Angles within a shape

Compare and order acute, obtuse and reflex angles

Reading angles on a protractor (Part 1)

Reading angles on a protractor (Part 2)

Reading angles on a protractor Part 3

Draw angles with a protractor 1

Draw angles with a protractor (Part 2)

Calculating angles within a shape (Part 2)

Calculating angles within a shape 3

Revision and Angle fluency facts

What does an angle measure?

How many angles does this shape have

Which shapes have a right angle (tick 2)

Which angles are obtuse (tick 2)

How big is angle B?

What is the approximate size of an internal angle of this regular pentagon?

Which is the smallest angle?

A numberline starting at 0 and ending at 100 is divided into 10 equal parts. Each equal part represents:

0.7 of a container is filled with water.  How much of the container can still be filled?

Lesson overview:Calculating angles within a shape 1

Core Content

Angles: