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

What type of triangle has 3 different angles and 3 different sides

What do angles inside a triangle add up to?

What are the size of the angles within an equilateral triangle?

What is the size of angle a?

What is the size of angle b?

Calculating angles within a shape 1: triangles

﻿Hello. My name is Mr. Kelsall and welcome to today's lesson about, Angles within a shape. Now, before we start, you will need a pen and a piece of graph paper. Also, please try and find yourself a quiet place somewhere that where you won't be disturbed. And don't forget to remove any sorts of distractions. For example, put your mobile phone on silent or move it away completely Pull the video. And when you're ready, let's begin. Today's lesson is all about, calculating angles within a shape and specifically looking at quadrilaterals. And I start by looking at types of quadrilaterals and then go look at angles within shapes and finally the angles within quadrilaterals. And after that, it's quiz time. I've already mentioned that you only need a pencil and a piece of graph paper. Now our star word we'll be talking about, particularly up into angles. We'll be talking about three types of triangles. scalene, isosceles, and equilateral, and our quadrilaterals are a parallelogram, trapezium, rhombus, square, and a rectangle. If you want to access this lesson, you will need to understand some basic facts about angles. You need to understand that a Right Angle is 90 degrees. A straight line is 180 degrees, angles around a point add up to 360 degrees and opposite vertically opposite angles are equal. You'll need to know the angles inside a triangle, add up to 180 degrees. And you'll also need to know that you can use properties of the triangle to find the missing angles. For example, the blue triangle on the screen talks about it's an isosceles triangle as a 40 degree angle at the top, and we need to find the two base angles which are equal so we can do 180 degrees take away 40 degrees, gives us 140, divide that between the two equal angles. So each angle is 70 degrees. Okay. Pause the video and have a look. What shapes you can see within this picture? when you're ready, press play to begin. Okay. So we've got some very basic shapes. I'm sure you've found lots and lots of different ones I'm drawing on the screen at the moment, a square. I know it's a square because it counts on two, three, four squares down and four squares along. So I know that all these Encore, all these sides are equal size. I could find a triangle here and I'm thinking about what type of triangle is, or I can see that I've got one, two, three, four down, and I've got one, two, three, four across that makes an isosceles triangle. Some people think this might be an equal natural triangle because this line at the bottom is four squares across. However, please remember that a diagonal of a square is longer than the base or the height of a square. So actually this line at the bottom, and you can see it. It's longer near the two lines. Therefore this is not an equilateral triangle, This is an isosceles triangle. I'm sure there's lots more shape to know, that you can find. And I'm sure you've found what's. Now let's come on to our main types of quadrilaterals. I've identified five main types of quadrilaterals, and I've looked at the properties and I'm comparing the angles of the quadrilaterals. And I'm comparing the sides of the quadrilaterals. Pause the video, have a read through this slide. Just think about what it means for it to be these shapes, what these shapes look like, what the properties of these shapes are. And then when you're ready, press play, and we'll start drawing some. So I'm looking at some of the shapes and the first two shapes that I can say about the squares. Now you will commonly see a square like this, four equal sides and four equal right angles. You won't often see a square like this. However, if you look, each one of these sides is equal because it is one diagonal on each side, therefore all the sides are equal and all the angles are equal. It must be a square. You can draw lots of different squares. For example, I could have a square, which is a two by two square. Now I can see I've gone to a long and it's two diagonals long on each side. And because these angle, these sides are equal. It makes it a square. The other property of a square is, it's got four, right angles, four equal angles. Well, how do I know that these angles are right angles? Well, actually the square within the square is divided into two the diagonal makes 45 degrees and I have two diagonals. So the two diagonals make 90 degrees. So I know each one of these angles is 90 degrees. Well then look at my next shape, a rectangle, but I can see that these rectangles all have 90 degrees because they're calling rough from the small squares. The difference between a square and a rectangle, is a square, has four equal sides. Whereas a rectangle has two equal sides and two other equal sides. And you can see how I've written this. I've got a little dash for the two lines, which are equal size, and I've got another, I've got two dashes for the lines, which are different equal size. And this is the same with all my rectangles. I can see this is the third shape is a rectangle because it's for long and three down. Our third shape isn't rhombus. Now, the way I like to think about a rhombus, is like a square. It's got four equal length sides. However, it doesn't always have 90 degrees, as the angles. What I tend to find, it's like a square, which has been stretched a little bit. So I have a look at this first shape. I know I've got four sides, which are equal. And I know this because if I count the diagonals and too long for each one, not too long, too long, one down on down , to a long two, a long one. So I know all these are going to be equal length because of that, I know that this angle and this angle are the same and the angles at the top and bottom are the same. So the only difference between a rhombus and a square, is that a square has four angles, which are 90 degrees. Whereas the rhombus has been stretched a little bit and the top and bottom angles are equal on both sides. Angles are equal. If you'd like to explore this a bit more, it'd be interesting to have a think about is a square. a rhombus and is a rhombus, a square. If you want to investigate that, pause the video and have a think about it. When I look to my next shape, I looked a parallelogram and properties of a parallelogram is it has two pairs of equal parallel sides. When it has equal parallel sides, it means the sides which equal one, and also which are parallel. Now we know that for size which are equal, we put a little line on that line. Sides which are parallel. We put an arrow on that line. I can see in a parallelogram these sides, which are equal, And that also parallel. So I'm going to put my equal signs on and show that they are parallel. Now you can see that, I guess, really, really messy. So just be aware of these properties of a shape. You don't always have to label them, but you have to understand that a parallelogram has sides has two pairs of sides which are equal and two pairs of sides which are parallel. The reason I make a bit of a point, about the sides being parallel is unequal is because of a trapezium. A trapezium has at least one pair of parallel sides. So I can see on my last shape, these sides are parallel, but I can also see that they're not equal. Please be aware of that again. I can see I've got some parallel sides there, but neither of these are equal. So now we've taken a little bit of time to look at what types of quadrilaterals there are and the props of these quadrilaterals. Have a look and go back to the shape that we started the lesson with and see if you can find any of these shapes within the shape on the screen, pause the video and when you're ready, press play continue. I think a square is nice and easy to find because we can start with whole shape and say, well, this is definitely a square Rectangle was very easy to find. Just needed to check the definition. Does it have four right angles? Yes It does. Des it have two pairs of equal parallel sides? Well, these ones equal that also parallel. These ones are equal. And that also parallel. And I'm really struggled to find a rhombus because when I started to think about it, I thought is a rhombus. A square is a square rhombus. And I looked at this shape in the centre and I thought, well, that can't be a rhombus because it's a square. Then I went back to the definition of a rhombus and I said, well, let's have a look at its angles. Are there two pairs of equal angles? Well, not equal That's one pair of equal angles and that's equal. That's my other Pair of equal angles. So I asked myself the next question, have I got four equal sides? Which four equal parallel sides? Well, those are all equal sides because I know I'm pointing one, two, three, four jumps on each one. So now I've got four equal sides. And I know that the first line here, is parallel with this line here. And I know this line here, is parallel with this line here. So actually when I think about it, and I look at the definition this shape, although it's a square, it's also a rhombus implement X shape. I thought, okay, I'm looking for a parallelogram and I couldn't really see any parallelograms. Like you normally see a parallelogram. So I started thinking about my definition again. I thought, well, actually, is this shape here? A parallelogram I want to ask ourselves, do we have two pairs of equal angles well I'll say equal and that's equal. And I forgot two pairs of parallel sides. Well, that's parallel. And that's parallel. So actually this is a parallelogram. And then I thought, could I find any other parallelograms in this shape? And then finally I thought, just going to draw my own shape to make sure, I can remind myself what a parallelogram traditionally looks like. So I drew a shape there and I thought, this is a parallelogram because it's got this pair of angles, which are equal. this pair of angles, which are equal. And it's got a pair of parallel sides and another pair of parallel sides. So I want you to keep thinking about, what is the definition of these shapes. when looking for a trapezium, I know that a trapezium has at least, one pair of parallel sides, so I'm going to draw a trapezium here. Now I know that this line and this line parallel, I've also noted that it isn't equal, but they're just parallel. There's all the trapeziums you can find in there as well. And all these trapeziums look very similar, just tilted on its side. And again, I've labelled my parallel sides. Moving on to our developing learning section of today's lesson, have a look at these shapes. What do you notice about the angles in the shapes? Pause the video and when you're ready, press play to continue. Okay. The first shape we've seen lots and lots, and we know that it's a square, for equal sides, for equal right angles. I've then taken this square and I've cut it into half. Of course it, because 10 to half I've dissected a right angle into two equal parts. So each of these angles here must be 45 degrees. So I start to thinking around that, then shape number three. I realised I've got a right angle at the top, and I've got an angle of 45 degrees and an angle of another 45 degrees. And I thought, I'd check this. So I thought do angles in the triangle, add up to 180 degrees yesterday. Do, did these angles have up to 180 degrees, 45 and 45 is 90 add another 90 is 180 degrees. Then I really started to think about this and I thought I'd take my two triangles from shape number three, and then put them together with shape number one. And I did that. I came up with shape number four, I'm going to start to think about, what are the angles in these shape? Well, I started with this one and actually I know that this is a 45 degree angle, and I thought this shape is a parallelogram. So I know this angle is 45 degrees, but I really struggled working out what this angle was. I know because it's a parallelogram, it's the same as this angle, but what is it? As I looked carefully, I realised that I had a 45 degree angle here and I had a 90 degree angle here. So I added the both together and that gave me 135 degrees, but I wasn't confident. So I wanted to check it on my other angle. And again, I looked and I could see I've got my right angle there and I could see how a 45 degree angle there, which is 135 degrees. And then I thought what does this parallelogram, what does this quadrilateral, I don't see what do its angles add up to? So I said I've got 45 and 135. That's 180. 45 and 135 that's 180. So this,quadrilateral has the internal angles of 360 degrees and carried on thinking about it a little bit more. And I went to picture number five and I removed all the lines that I didn't need. And I know that 45, 45,135, 135. use the information that you've just learned to try and find the missing angles and shape number four, pause the video when you're ready, press play to continue. Well, I know I have a right angle here. I know this angle is 45 degrees. I know that for one of two ways, first way is half of a right angle. Second way. If I look at my shape here, I know that I've used that shape, so this angle must be 45 degrees in the same way, This angle must be four to five degrees. I can check this does 90 degrees at 45 degrees , at 45 degrees a total of 180. Yes, it does. It's worth noting at this point that we're just looking at squares. We're not looking at rectangles. And the reason I say that, is because if I look at a rectangle, if I look at my first angle there, it's not 45 degrees. This is not 45 degrees because the size of different lengths, that angle are not going to be split in a right-angle exactly into half. Therefore these angles won't be 45 degrees. Okay. Have a look at the shapes that you've got on the screen. Can you find angles within these shapes? It's worth noting that some of the angles you will not be able to find. some of them you'll be able to find it a lot of right angles and a lot of 45 degree angles. And if you can find the 45 degree angles, you can find the 135 degree angles. So see if you can find those three angles, 90, 45,135, pause the video. And when you're ready, press plates continue. Okay. Very quickly. And all of my squares and all of my rectangles, I know that each of these angles are 90 degrees. So I don't need to spend too much time looking at those. A lot of my new learning to say comes from Rhombus parallelogram and trapezium. Now I don't know and I can't work out the angles of any of these rhombuses yet, because I don't understand the properties about them, to find that out. So I'm going to leave those for the moment. However, In a parallelogram. I can see I've got a 45 degree angle because I've got half a right angle. I can also see 135 degree angle there because I've got a right angle and half a right angle. So 90, 45 and 135. However, I can't tell what dangles off of these shapes, because I don't know how I got half of the right angle, a third of the right angle or what I've got there, In a trapezium, I can find some angles here, but not many. I can see I've got a right angle there, but I can't find the angles of these without measuring them. And the same with these, I don't know what these are just yet. I did this slide to prove a point. I need you to understand that angles inside a quadrilateral add up to 360 degrees. If you're happy with that and you understand how it works and you find using it, then you can carry on. if not pause the video now, and look at these angles , with your protractor measure, all of the angles inside these shapes. And when you add them all up, you'll find that they'll add up to 360 degrees. So pause the video when you're ready, press play to continue. Okay. So like I said, angles inside a quadrilateral, add up to 360 degrees. And I can say this because a quadrilateral is made of two triangles and each triangle is 180 degrees. Let me give you an example of how to draw this and how you can see the two triangles within a quadratic model. And then I'll ask you to draw also. I'm going to draw quadrilateral, which is a shape with four sides of drawn a trapezium here. And I know this because it's got two pairs. So one pair of parallel sides. Now I need to find two triangle in this shape. So I can point to any Vertices. I'm going to choose this Vertice here. And I'm going to draw a line from that Vertice to every other Vertice. Vertice means corner. So the first line I've drawn, second line I've just started a third line is here. Now when I've drawn a line from that Vertice to the other three vertices. I can see that I've made two triangles. I know angles inside a triangle add up to 180 degrees. So I know the angles inside a quadrilateral add up to 360 degrees. You can do that with any triangle, any quadrilateral you want, it doesn't have to be a regular quadrilateral or any chronic quadrangles we've talked about. I just need to join a vertice join that line to all the other vertices. And I can see that I make two triangles of 180 degrees. So they add up to 360 degrees, try and draw some quadrilaterals for yourself and find the triangles within the quadrilateral to prove this, pause the video, and then when you're ready, press play continue. And that brings us to using this idea that angles inside of quadrilateral up to 360 degrees, have a look at the quadrilaterals on the page and see if you can find the size of the missing angle. You've been given three angles. So the fourth angle, you'll need to work out what the three angles add up to. And then the fourth one to get to 360 degrees or do 360 degrees take away the other three angles, pause the video. And when you're ready, press play to continue. And my first shape, the three angles add up to 200 and sorry, 310 degrees. That means that the fourth angle is 50 degrees in my second shape. I know that 120 at 60 and 60 add up to 240, which means that my missing angle must be 360, take 240, which is 120. I also know this is my mission and goal because actually this is a parallelogram. I can see that my opposite angles are equal and if I remind myself of what other properties of the parallelogram. I've got one pair of parallel sides. I've got another pair of parallel sides, and I've got two opposite angles, which are equal. So this must be a parallelogram. And my final shape, 135 and 45 and 60 has 240. So we're missing angle must be 360, take 240, which is 120 hour independent task for today. It's all to do with finding the message angles in these shapes. You will need to use a combination of angle properties, which you know, like 90 degrees, 45 degrees, 135 degrees, as well as angles inside a quadrilateral. Add up to 360 degrees. You'll also find it useful to think back to angles that we revised in the beginning of you've learned before and going on a straight line, vertically opposite angles, things like this, pause the video when you're ready, press play to continue. And your answers are on the screen now, congratulations on completing your task. If you'd like to please ask your parent or carer to share you with on Twitter, tagging @OakNational and #LearnwithOak before we go, please complete the quiz. And so that brings us to the end of today's lessons on angles within a shape, a really big world on all the fantastic learning that you've achieved today. Now, before you finish, perhaps quickly just review the notes that you've made and try and identify the most important part of your learning from today. Well, all that's left for me to say is, thank you very much. Take care and enjoy the rest of the learning for today.

What type of quadrilateral has 4 equal sides and 4 equal angles?

What type of quadrilateral has 4 equal sides and 2 pairs of parallel sides?

What type of quadrilateral has 2 pairs of equal angles and 2 pairs of equal parallel sides?

What do angles inside a quadrilateral add up to?

What is the size of the missing angle in this quadrilateral with angles: 90°, 120°, 40°, ?

Calculating angles within a shape 2: quadrilaterals

In this lesson, we will learn about different types of quadrilaterals and how to calculate angles within composite shapes.

Maths

Y5 Maths

Key Stage 2

Year 5

Calculating angles within a shape (Part 2)

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 on a line or around a point

Calculating angles within a shape 1

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?

What is the size of the missing angle?

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 (Part 2)

Core Content

Angles: