# Lesson video

In progress...

Hello everyone, my name is Mr. Kelsall.

Now, before we start you will need a pen, a piece of paper, and a protractor.

Also, please try and find a quiet place around the house somewhere that you're not going to get disturbed.

And don't forget to remove any sort of distractions.

For example, put your mobile phone on silent or put it away completely.

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

So today's lesson is reading angles on a protractor.

We're going to look at measuring reflex angles.

Then calculating the reflex angle.

We'll then use both of these skills to measure angles within a shape.

And finally, it's quiz time.

You'll need a pen, piece of paper, and a protractor.

We'll also use the words right angle, acute, obtuse, and reflex angle.

Protractor, the baseline of the protractor, the crosshairs of a protractor, the vertex or vertices, meaning the corner or corners of an angle.

You also need to know some facts before we access this lesson.

You need to understand that an angle is where two lines meet.

Turn means to rotate around the point.

You can talk about a full turn, which is 360 degrees, a half turn 180 degrees, then a quarter turn, which is a right angle, 90 degrees.

You need to understand that an acute angle is less than 90 degrees.

A right angle is exactly 90 degrees.

An obtuse angle is between 90 and 180 degrees.

A straight line is 180 degrees.

And a reflex angle is between 180 degrees and 360 degrees.

We'll talk about three shapes, a quadrilateral, a four sided shape, a pentagon, a five sided shape, and a hexagon, a six sided shape.

You'll also need to know how to use a protractor.

You'll need to be able to read from both sides of the protractor and measure angles and areas, 10 degrees, five degrees, and one degree.

And now for our new learning for today.

So the first way to measure a reflex angle is to start with a straight line and add on the extra bit of the angle.

So here, I'm looking at my reflex angle, which is all the way from here to here.

Now I know that if I put my protractor on there, and I line up the vertex, the baseline, I know that all the way from there, all the way around to here is 180 degrees.

But do I really need to measure that? Or do I just know that angles on the straight line add up 180 degrees? So I can just think this line here is 180 degrees and I can just add on this little bit extra here.

So I'm going to do 180, and I'm just going to add on this bit, so I'm reading my protractor upside down by crosshairs, baseline, crosshairs, baseline.

And this time on going 10, 20, I think that's 21 degrees.

I'll spin my protractor around and I'll double check that I can measure it accurately.

So I'm going crosshairs, baseline, crosshairs, baseline, 10, 20, 21 degrees.

So I know that part of the angle there is 21 degrees.

I then need to add up my 180 degrees.

Add on my 21 degrees, should give me 201 degrees.

So I know the reflex angle, there is 201 degrees.

The second way that I can measure a reflex angle is by starting with 360 degrees.

That means knowing that as I turn around the point that whole angle is 360 degrees, and then I'm just going to take away the bit that I don't use.

So in this case, I'm going to start here measure all the way around to there knowing that's 360, but then I'm going to take away this part of the angle.

So I start with 360 and I only need to measure this acute angle, sorry this obtuse angle here.

Crosshairs, baseline.

I read it all the way around to 150, 155, six, seven, eight, nine, 169 degrees.

As always I can double check it.

So I'm going to start reading from this side this time.

So crosshairs, baseline, 10, 20, 50, 159.

Okay, so I've made a mistake, so let's double check it.

So zero, baseline, crosshairs.

Starting from zero going all the way around, ah, there's my mistake.

It's one of the common mistakes that I mentioned earlier.

So earlier I said, we count overall we count below.

I saw 160 and I went down one.

So I've said 160, 169.

And I know that's incorrect.

One less 160, is 159.

And that makes sense because that's what the second angle was.

So if ever you need to check something, always check it.

So this angles 150, 155, six, seven, eight, nine, 159.

Okay, but I haven't finished.

I've only found the size of this angle and actually what I need to do is find the size of this angle here.

I'm going to start with a 360 degrees, and I'm going to take away 159 degrees.

You can either use a written method like this.

I think nine is one, five take five is zero, three take one is two.

If you don't want to use a written method and you just want to use a mental method, start at 159 and think, what do I need to do to add on, to get to 360? Well add one, it takes me to one 160.

Remember that one.

How many do I need to have to get to 360, well I need to add on 200 more.

So 200 add my one is 201 degrees.

Now we need to develop our learning, have a go at these angles, try and measure these reflex angles.

Some will be more suitable for finding a straight line and adding on the difference.

Others will be easier to find the full 360 degrees and take away the acute angle or the obtuse angle.

So for this one, I can see I've only got a small angle here, so it's nice and easy to measure this small angle, this acute angle, which when I line up my crosshairs, baseline and all the way around 30, 35, 36 degrees.

Once I've labelled my 36 degrees, I'm thinking my 360 degrees take away my 36 degrees.

So my angle is 224 degrees.

However, if I compare this next angle, I can see it's probably easier to draw a straight line here.

So I know this parts are 180 degrees and then I'm just measuring the angle here.

I'm just going to extend that line a little bit so that it's easy for me to work with.

So crosshairs, baseline, crosshairs, baseline, and I'm reading on the outside.

I've got 10, 11, 12, 13, 14 degrees, 14 degrees.

This angle here is 194 degrees.

I'm looking at this angle here.

And again, I feel that this angle lends itself to doing the 180 degrees, we'll just dump it there, add on the acute angle here.

So I'm going crosshairs, baseline, crosshairs, baseline, reading from the inside 10, 20, 30, 35, 36, 37, somewhere between 37 and 38 degrees, I'll say 38 degrees.

I can do 180, 190, 200, 210 that's adding 30 and I've got eight more to add, so 218 degrees.

And my final one, I feel it's easier to measure the angle there and take it away from 360.

So crosshairs, baseline, crosshairs, baseline, and reading from the outside, because my zeros here, 80, 81, 82, 83, somewhere between 83 and 84, I'll say at 84 degrees.

And then again I'm doing my 360 degrees take away my 84 degrees.

Ten take four is six.

15 take eight, tricky one, people always struggle with it's seven.

Two take zero is two.

So this angle here is 276 degrees.

And now it's time for our independent task.

And now the task is over to you.

Can you measure the angles inside the shape? I'm only really interested in this angle here, this reflex angle, because that's what I'm practising today.

So I'm going to use two methods to do this.

Method number one, I'm going to extend that line a little bit, extended a bit more so I can see it accurately.

So crosshairs, baseline.

I know that's 180, so I'm just interested in this part of the angle here.

So crosshairs, baseline, reading around from the other side to there, 80, 85, 86, 87, 88.

I know this part is 88 degrees, add on my 180 degrees.

Well, I can do this mentally.

I can say 180 add on eight is 188.

180 add 80, 190, 200, 210, 220, 30, 40, 50, 60, so I have 268 degrees.

I can do the same with my two other reflex angles.

This time I've noticed this angle here is an acute angle.

I'm just going to measure that and do 360 take away that.

So crosshair, baseline, read around, 65, 66, 67, maybe 68 degrees.

So if that angle is 68 degrees I'm then thinking 360 degrees take away 68 degrees.

Well I know 360 takes 60 is 300 and just need to reduce it by eight more.

So I know that's 292 degrees.

And my angle here I'm going to do it back to my first method.

And I'm going to extend it.

And I know that's 180 degrees.

So I just need to add on this acute angle here.

Again, if you need to extend this line, extend it, you notice it's gone off there.

When I put my protractor on I'm going to read from here, not there.

In fact, I'm going to extend it a little bit further.

So it's clear and it's neat.

So this time I'm going crosshairs, baseline, count around 10 20, 30, 40, 45, 46, 47, 48 degrees.

Does that look correct.

So I've got 180 add on 48.

I know 180 add 20 is 200, add on 20 is 220, add eight is 228 degrees.

So I know that angle is 228 degrees.