The mathematical object to measure an angle is...

A standard protractor (the one that was used in the video) measures from 0 degrees to...

If I accidentally measured an angle from 180 degrees instead of 0 degrees, then I noticed that it measured to 150 degrees, what would the angle truly measure?

The middle point of the mathematical object, where we line up the point at which the two lines meet, and where we measure an angle, is called...

I measure an angle accidentally from 85 degrees instead of 0 degrees and it measures 112 degrees. I have done this as accurately as possible. Does this mean that my angle is 27 degrees?

Describing and comparing angles

﻿Hello and welcome to the lesson about angles, measuring and drawing angles. I want you to take a moment to remove any distractions that you may have, whether that be your brother, your sister, you know your pets, anything that could be distracting you. Make sure your phone is on silent as well, as mine always is. And make sure you are not getting distracted throughout. Turn all those app notifications off, whatever it may be. It needs to be turned off so we can do that really powerful math that we always do. One thing I must stress beforehand though is that we need a protractor. So, so important that we have a protractor, you can get one from any good high street retailer you can get one from online, wherever you may find one. Okay, so important, that's what we use to measure and draw angles. As we've learned previously, and as you may . So without further ado, it's time for me to take you through how to do this. So let's get started. So let's have a go at the Try this step. So the students below got these angles wrong can you explain why? Pause the video now and have a go. Fantastic. Let's get through why these students could potentially be wrong. So did you find out why Cala could potentially be wrong? Hm, what has she done here? So she's actually if you see it she hasn't measured from zero. If you notice she's actually measured from, what's that number going to be just there. What's that number going to be? It's going to be 15 right? So that one there she's measured from 15 through to 60. So she's right with that that there are 60, but unfortunately she hasn't measured from zero. So she needs to measure from zero. So the difference between 60 and 15, is going to be what would that be? 45 right? So 45 degrees that angle actually is. So we can explain that by saying that she has not measured from 40 sorry from zero degrees. She has measured from 15 degrees. Heck, you can even be really, really enthusiastic and put an exclamation mark at the end, how nice. So for B, for Xavier. He said his angle was 135, what did you get for him? He seems a little bit strange for what that is. That's quite a small angle. We know something that looks like that is sort of an acute angle isn't it? So we need to think, well he must be wrong because he's just said an obtuse angle. Just by a sort of like, logic and definition there. So he's actually measured from the inside, you should never measure from the inside. So going from zero through to that gives us the angle of 45 degrees. 45 degrees there. So we can say he has measured from the inside not the outside. And finally we've got Zaki down here who reckoned that the angle he has drawn is 37 degrees. What do we reckon to that one there? 37 degrees. Has he got that wrong? Well unfortunately he has. It looks really good to begin with because this almost had me fooled. Right, it looks really good to begin with. It goes from zero through to 37 but look where the crosshair is. Right? This thing here. It should be lined up and it should be here instead. So he has not got we should say actually, good grammar and punctuation here, we should say he has with a lowercase h, that he has not got the crosshair spelled my crosshair wrong, silly me! So he's not got the crosshair lined up correctly. Fantastic. Let's move on then. So we should understand that now. Now, I've got some space for here for you to work, do all your working out so you see what I'm going to do on an interactive protractor, so let's get to it. So let's just draw anything that looks vaguely like this and I'm happy. Okay? Doesn't have to be accurate, and we don't know how accurate it is just yet. We don't know what the angle is. So, once you've drawn that out what I'd like you to do is I'd like you to place your protractors as I'm doing. The number one thing you need to do is you need to make sure that the angle has what we call the crosshair nicely lined up with the two where the two lines meet. So if I zoom in I can really see I'm measuring where that crosshair actually is. So you can see it's pretty much bang on there. Right? Now if I started measuring from here I wouldn't get the angle correctly. You think why, just for one minute have a think why. Why could that be? Well the key reason is the fact that I'm not measuring from zero. Currently I'm measuring from, well look at that, looks like 30, 32? Maybe? No sorry, 37 degrees. My apologies, 37 degrees. So we've got this five mark there, one, two across for 37 degrees. Now, I need to measure from zero of course, So I need to take my protractor round. So, but be really careful, keep it nice and lined up on the crosshairs still but rotate it round. Just start from zero here, I then need to turn around. So remember angles are all to do with the turns. Right? So it's a measure of turns. So turn around zero degrees all the way around and I get to approximately don't need to be 100% precise here but I get to approximately 121 degrees, you see it's just shy of 121 degrees. So that's how we use our protractor. I could adjust my angle, I could do, I could shoot it off over here. And actually, we discover that that one there would be a perfect right angle. So, we've got all different ways that we can measure angles right? We've got to make sure though regardless of what we're measuring we always measure from zero, and we do it as a measure of turns, and that we go around. You could for example, get it from 180 through to 90, just do 180, subtract 90. So if you mistakenly put your protractor like this and you counted in from 180 and got it to 120 there, you'd say well it should be an angle of 60, but you could do 180 subtract 120. And that'd give you that angle of 60. So you may have some more problem solving based questions that could be involved with that. So just be aware. So remember, crosshair lines up so that the two lines intersect, and of course measuring from zero throughout. Okay, let's get back to it. So you've got this now, Independent Task that you need to complete. So what I'd like you to do is I'd like you to fill in those blanks for the following exercise. You may want to go back in the video for some help. So if you need to go back to the interactive part of the lesson where we needed that protractor, by all means please have a go, and pause the video and have a go. Excellent. I'm going to assume that you've done that. So I'm going to go through the answers now. We need to think, we can use a blank to measure an angle. What was it? What did I say, what did we use? What was that mathematical instrument we used? It was a protractor, wasn't it? So we can tick that one off. So we can use a protractor to measure an angle. For example in order to measure angle A, angle A is that, we can use the blank scale to see what? That it has a value of blank. Well, I'm measuring from zero aren't I all the time, so I need to measure all the way from zero to here, there we go, all the way to, that looks like 75 to me. Aha! We have an answer on 75. So 75 degrees. Of course we always measure angles in degrees. So in order to measure angle B we can use the blank scale to see that it has a value of blank. Well, what scale should we use to begin with here? Missed that one out didn't I, silly me. Seriously Thomas what's up, what am I doing? We can use the, what did we use here? We used the outer scale didn't we? We used that outside part. The outer scale. Or the outside rather. So outside, we can take that off. And then the inside scale we're going to use for B and of course if we do that we measure from zero don't we? We measure from zero to here. Then we go all the way around and we see that that has a value of, 100 would be up to here, and then I can see it go to five more sort of like little tiny notches across, so I can see it has a value of 105 degrees. So mark it right or wrong, I really hope you got it right. Let's keep going. So you have your Explore Task to complete. It says both of these students have incorrectly measured the angle. That's a really important statement there. Both of those students have definitely incorrectly measured the angle. So I'm not trying to trick you here, it may seem like one of them is correct, just be really, really careful about what marked angle actually is. So I think the angle 115 degrees, that's what Yasmin's saying, and then Bihn's angle is saying 65 degrees. So pause the video now if you think you know what you're doing. If you don't know what you're doing, and you need support by all means, or you want to go through the answer, by all means stick around and I will help. So pause the video now and have it go as you need to, or listen in. Right, so I'm going to go through this now, and give you a little bit of support whilst I'm doing it. So we need to think, how could we have arrived at an angle of 115 degrees? Well if I look round, I see that that is going to be marked on as 115 degrees up to that point there, if I'm using the, what scale? The outer scale, or the outside scale. So that was 115 there, so that's how we've got Yasmin's answer of 115, she's just measured from the outside. So she measured from the outside. The outer scale. Now, Bihn's statement is a little bit difficult, it says how could we arrive at that one, because on the face of it, now I'm really, really keen on highlighting that they are both incorrect. On the face it looks correct, almost had me fooled as well. Is that if I'm measuring from zero I'm going to go all the way around and we hit of course 65 degrees there, so surely that's correct right? Right? But she hasn't measured the marked angle right? The marked angle is this thing here, that is what we're focusing on right? So if I colour that in you can hopefully see that now, very, very clearly. That is the marked angle. So we need to be measuring this thing. Now that sort of sector taken there, we have there a sort of like a convoluted circle of some description is 65 degrees. Now we know that angles, you may have learned this from a primary school actually, angles around the point sum to what? Can you remember? What do they sum to? 360 degrees right? So really important you're able to recognise that. You've got a point here and then we're going all the way around that turning point down there, okay all the way around, and we're saying well that of course is going to be 360 in total. So we need to subtract 65 degrees from that. So the actual answer is going to be 360 degrees subtract 65. Now I'm going to let you think about it just for a moment, whilst we formulate an answer of why, Binh's answer to arrive at the correct measurement is going to be this. So we can say she has got 65 degrees but it is not the marked angle. So 360 minus 65 you should know that, that of course is 295 degrees. So we know the actual answer is 295 degrees. How fantastic, we've got a really nice problem solving question there, also have some description. Let's carry on then. Unfortunately that brings us to the end of the lesson then. So I just wanted to say you've done an amazing job as always. If you've managed to keep up, really, really good job. Don't forget to smash that exit quiz. So you can just show us all at Oak, and indeed your teachers, and the entire country how well you're doing overall right? Please make sure you do that so you can test how much you've learned. And remember, stay safe and take care. Bye bye.

Which of the following best represents the definition of the word 'angle' in mathematics?

A full turn represents how many degrees?

Three quarters of a turn would represent how many degrees?

Two thirds of a turn would represent how many degrees?

If I were to turn 0 degrees, would I change direction at all?

Measuring and drawing angles

In this lesson, we will learn how to use a protractor to measure and be able to draw angles.

Maths

Y7 Maths

Key Stage 3

Year 7

Angles

Geometry

THEME

UNIT

Partitioning angles

Finding unknown angles

Exploring intersections

Transversal angles

Alternate angles

Corresponding and allied angles

The space BETWEEN two lines is called the...

The space OUTSIDE two lines is called the...

Two lines cross and form an intersection. One of the marked angles is 75 degrees. The vertically opposite angle to 75 degrees would be...

If Angle A is greater than Angle B, how can I express this mathematically?

You are given that: 360 - R = S. Which of the following statements is correct?

Is it possible to draw a hexagon with three pairs of parallel sides?

Is it possible to draw a triangle with a pair of parallel sides?

Alternate angles only appear in the interior region.

Allied angles are equal.

If I have an equilateral triangle and a square around a point, what is the remaining angle left?

Lesson overview:Measuring and drawing angles

Core Content

Angles: