REVISION: Which of these angles is obtuse?

Which is the smallest angle?

Is this statement always, sometimes or never true: "I can draw a triangle with 2 obtuse angles"

How many acute, obtuse and right angles are there in this shape?

Is this statement always, sometimes or never true: "A quadrilateral has 4 acute angles"

Angles inside a shape

﻿Hello everybody, my name is Mr. Kelsall and welcome to today's lesson about comparing and ordering acute, obtuse and reflex angles. Now before we start you will need a pen and a piece of paper or something to write on. You will also need a piece of graph paper or squared paper, and you can print this out from the slides if you need. Also, please find a quiet place around the house somewhere where you won't be disturbed and don't forget to remove any sorts of distractions, perhaps put your mobile phone on silent or move it away completely. And then if you can pause the video and then when you're ready, let's begin. So today's lesson is all about comparing and ordering acute, obtuse and reflex angles. Well we need to start by understanding what is a reflex angle, we need to be able to identify reflex angles within shapes, we need to be able to draw reflex angles, and after that, it's time for your quiz. I mentioned already, you will need a pencil, piece of paper and some graph paper or squared paper. Our star words for today, the words we'll be using throughout the lesson are right angle, that's an angle at 90 degrees an acute angle is an angle measuring less than 90 degrees. An obtuse angle is an angle measuring more than 90 degrees but less than 180 degrees. Our new word will be reflex angle, interior angle and exterior angle. So in order to access this lesson you will need to know a little bit of previous learning. The first thing you need to understand is that an angle is the point where two lines meet. Have a look at your example here, this angle, the two lines meet, however here, the two lines do not meet and therefore they do not create an angle. Secondly you need to understand that the word turn means to rotate around a point. So it means to move around a point, you'll often hear people say turn around. Now a full turn means a full 360 degrees. 1/2 turn means 180 degrees and 1/4 turn means 90 degrees. You'll notice that 90 degrees we mark with a little square in the corner, rather than a semicircle. You'll also need to understand that an acute angle is less than 90 degrees. So I can see this angle here is less than 90 degrees. If I've got an angle there, I can see that this angle here is less than 90 degrees. An obtuse angle it's between 90 degrees and 180 degrees. So if I've got an angle like this, I can see the angle there is obtuse, I can see that this angle here is obtuse. If I look at my shape on the right hand side I can see that I've got angle number one is an obtuse angle, angle number two is a right angle, three is acute, four is called reflex and that's what we'll learn about today. Five is an obtuse angle and six is an acute angle. The words that we'll be using for shapes are quadrilateral, which is a four-sided shape, pentagon, which is a five-sided shape and hexagon, which is a six-sided shape. Be careful with these shapes because if you look at the shape we've just talked about, I'm going to count the number of sides. One, two, three, four, five, a six-sided shape. Therefore this is a hexagon. It doesn't look like a regular hexagon we see but it is still a hexagon. So for our first task, have a look at the angles on the page. Some are angles, some are shapes. Can you try and identify what angles you can see? Have a look for acute, obtuse and right angles. Pause the video and when you're ready, press play. Okay if I look at the first angle, it is clearly marked as an obtuse angle. The second shape, if I look at the interior angles I can see all of the interior angles are obtuse angles. You'll notice how I used the word interior angles there to refer to the angles on the inside of the shape. Shape number three is a parallelogram, and I can see I've got an acute angle there and an acute angle there. I can also see that I've got obtuse angles there. Number four, this is not an angle, the two lines do not form to meet at a point so it does not create an angle. Shape number five is a quadrilateral is a square and I can see that in the corner there are four right angles. Because they're right angles, I mark them with a square. Shape number five, the blue angle. What's interesting is that actually, if I compare this, I know that this point here is a right angle. So you can see it sometimes marked as a semicircle or a quad circle, but the correct notation is to use that square which is a right angle. The green angle, I can clearly see as an acute angle, same with the other green angle, it's also acute. When I look at the triangle I can see that I've got three internal angles, which are all acute. And my final squiggle is not an angle because it does not have points where the lines meet. It does have a tiny point here, but since these are curved it's not a straight line it can't form an angle. So this brings us to our new learning for today, all to do with terms. Now we know already that an acute angle is an angle less than 90 degrees. And we know that an obtuse angle is an angle which is measured between 90 and 180 degrees. However, what happens beyond 180 degrees? Well this is called a reflex angle. And a reflex angle measures between 180 degrees and 360 degrees. So if I think about, as a turn, if I ask you to turn 270 degrees, I'm going to start here and I'm going to turn all the way around to here. If I look at here's an angle, there's my starting point, and I'm looking 270 degrees so I'm turning all the way around to here. So that is a 270-degree angle that is a reflex angle. You'll also see reflex angles in this shape. Again, I've come past 180 degrees, I'm going beyond 180 degrees to a little bit further. You might see a reflex angle like this. So we went all the way around from 90 to 180 to 270 and I keep going but I don't get to 360 degrees. These are examples of a reflex angle. Can you say this definition with me. A reflex angle measures between 180 degrees and 360 degrees. Here are some more examples of reflex angles. You can see how a reflex angle is bigger than 180 degrees but less than 360 degrees. Can you pause the video and have a look around the room and see if you can find examples of reflex angles around the room. Now that we understand the definition of a reflex angle can you have a look at these shapes? Have a look at each angle in the shape and see if you can find any which are reflex angles. And then find how many reflex angles you can find in total. Pause the video and when you're ready, press play. So I looked to my first shape and I thought "Are any of these angles here, a reflex angle?" And I looked to my first one I know that's an acute angle. And therefore that's an acute angle. And I looked to the other side and I realised they're both obtuse angles, so this shape doesn't have any reflex angles. I then looked to my second shape and I thought well I've got acute angle there, an acute angle there and I know that this is a right angle. However this point here, this angle here is greater than 180 degrees. So I found my first reflex angle. So this shape has one reflex angle. Shape number three, well that's very similar to shape number one, and I know shape number one didn't have any reflex angles. And finally shape number four, I've got an acute angle, and another acute angle another acute angle. I think I got an obtuse angle and I also got a reflex angle here. So this shape has a reflex angle, one reflex angle. By the way, do you remember the name of this shape? How many sides does it have? One, two, three, four, five. It's a five-sided shape so we call it a pentagon. Remember it's not a regular pentagon it's an irregular pentagon. So this brings us to our develop learning section of today's lesson. If you have a look at the angles, what do you notice about the angles? What's the same, what's different about this angles? And which is the largest angles? Pause the video, and when you're ready, press play to continue. So, I asked you to think what was the same and what was the different about these angles. Well, I've noticed one thing straight away they're all different colours. But I was trying to think what was the same. And if I look at them, I think they're all the same size. I think they're the same amount of turn. If I compare them I can see from there to there. If I try and draw the lines, the same length, I should be able to see that all of these are the same amount of turn. So they're all the same amount of turn they're just different colours. And also the length of the line is a different length and that's worth watch out for when you're measuring angles. X task have a look at these angles, what is the same? What is different? Pause the video and when you're ready, press play. So again, I noticed this time that they're all different colours again, but this time they're all the same length lines. And I've also wondered whether they're the same size angle. And actually they are, they're just turned around a different way. So again, as last time they're all the same size, they've got the same amount of turn in each angle. we move from acute angles we're now looking at these reflex angles. Same question, what is the same? What is different about these angles? Think which is the largest angle and which is the smallest angle too. Pause the video and when you're ready, press play to continue. If I look at all these angles I can see they're actually the same size angle. I can see the lines, some of them are different lengths, and I can see there some of their angles are rotated around different ways. However, there's an odd one out. Can you spot it? What's different about this angle here? Okay, so all of the other angles are reflex angles, the amount of turn they have is greater than 180 degrees, this is greater than 180 degrees, look where I'm stopping 180 degrees is there, this 1/2 turn is greater than 180 degrees. 180 degrees is there, is greater than 180 degrees. I'm going to extend this line, 180 degrees is there and it's greater. However, this angle at the bottom is not a reflex angle, it's an obtuse angle. I know it's obtuse because I know that's 90 degrees and that's greater than 90 degrees. I know that is 180 degrees, and I know it's less than 180 degrees, so it's an obtuse angle. Now we're to develop our learning. And we're going to look at which angles you can see within these shapes. It asks what are the interior angles of the shape? The interior angles are the angles inside the shape. Notice that this is a combination of acute, obtuse and reflex angles. But they are all interior angles because they are inside the shape. Okay, pause the video, identify acute, obtuse and reflex angles. Okay, I know the first angle is acute, reflex, acute, acute, acute. This angle is acute, acute, acute, obtuse. I think that's 90 degrees, but I'm going to check it. If I go back to my right angle measurer, does that work? This is acute and the final one is reflex. And if I remove my markings, I can see the blue angles are reflex angles, I've got an obtuse angle which is the green one and the others are acute angles. Now it's time for your independent task. You draw these shapes? The first shape is a quadrilateral with two internal obtuse angles. So internal angles are the angles on the inside of the shape, and two of those need to be obtuse angles. The second shape, can you draw a pentagon with an internal reflex angle? Can you draw a hexagon with two internal reflex angles? Once you're done with these three shapes try to draw all the shapes with acute, obtuse and reflex angles. Pause the video and when you're ready, press play. I'm going to just start with a quadrilateral with two obtuse angles. I'm going to draw my obtuse angles to begin with. I know if I do that I have one obtuse angle there and another obtuse angle there. However I've got three lines so a fourth line is needed to make it a quadrilateral. So you can see that I can draw a quadrilateral with two internal obtuse angles. Yours might look different than this, in fact it probably will look different to this, but make sure you've got the internal obtuse angles. Your next one is a pentagon with a reflex angle. Well I'm going to start with this reflex angle. So I know it's an angle of both 180 degrees, there's my reflex angle. I've got two sides at the moment, that means I need to add another three sides to make it a pentagon. So I'm going to go one, two, three. And let me just check that, I have a pentagon which is a five-sided shape and it has an internal reflex angle. Okay I've met the criteria. Again, yours will probably look different than mine but you must have the reflex angle and it must have five sides. And the final shape is a hexagon with two internal reflex angles. Okay so I'm going to start by drawing my reflex angles. I've got a reflex angle there and a reflex angle there. And I've used three sides and I need another three sides to make it a hexagon. So I'm going to join up, I'm going to go one side, two sides, three sides. Let me check, do I have two internal reflex angles? Yes, do I have a hexagon which is a shape with six sides? One, two, three, four, five, six. Yes I do. Again, yours will probably look different than mine but it must have the same criteria. That brings us to the end of today's lessons on comparing and ordering acute, obtuse and reflex angles. A really well done for all the fantastic learning that you've achieved today. Now, before you go, perhaps you need to review notes and try and identify the most important parts of your learning today. Well, all that's left for me to say is thank you, take care and enjoy the rest of your learning for today. Congratulation on completing today's lesson. If you would like to share your work, please ask your parent or carer to share you work on Twitter tagging @OakNational and the hashtag LearnwithOak. Before you go, don't forget to complete the quiz.

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In this lesson, we will learn about reflex angles, and then consider how to compare and order acute, obtuse and reflex angles.

Lesson overview:Compare and order acute, obtuse and reflex angles

Core Content

Angles: