Lesson video

Welcome to the first lesson in this unit, Missing angles and lengths.

Today we'll be finding the value of missing angles.

First of all make sure you have everything you need.

Just a pencil and a piece of paper for today's lesson.

Pause the video and get your equipment if you haven't already.

Okay, here's our agenda for today.

So we're finding the value of missing angles beginning with a quiz to test your knowledge from the previous lesson.

Then we're going to calculate angles on a straight line and then around a point before you do an independent task and a final quiz to test your learning.

Great work.

Now for our Do Now.

Calculate the degrees of rotation for each example.

In the first one a key is turned 40 degrees less than a right angle.

In the second one the key is turned three times.

And in the third one the key is turned half a turn.

Pause the video and calculate the degree of rotation for each example.

So for the first one we were dealing with a right angle.

We know that a right angle has a value of 90 degrees and your key turned 40 degrees less than that.

So all you needed to do here was 90 take away 40.

And I know that 90 take away 40 is 50 degrees, so your key was turned 50 degrees.

Okay, let me write that again.

It looks a bit less like 500.

There we go.

That's more a degree sign.

In your second example, the key was turned three times.

We know that a full turn is 360 degrees.

So if the key was turned three times we're doing 360 multiplied by three and you may have done a column multiplication.

Zero times three is zero.

Six times three is 18.

And three is nine plus the one is 10.

So your key turned 1,080 degrees.

And in the final one the key turned half a turn.

Well, if a full turn is 360 degrees, then half a turn is 360 divided by two.

And I know that 36 divided by two is 18.

So 360 divided by two is equal to 180 degrees.

Now let's start to think about what we know already about angles.

Look at this angle.

What do you know about it and what key vocabulary could you use to describe it? That's right, this is a right angle.

The symbol in the interior angle tells me this, so I know that this right angle has a value of 90 degrees.

Now if I put two right angles together, think about what we already know about the size of a right angle, what can you tell me about the angle described by the blue arrow? Well, the blue arrow represents two right angles, so I know that two lots of 90 is equal to 180.

And I used my related facts there.

I knew that two lots of nine were 18.

90 is 180 degrees.

So the value of this blue angle is 180 degrees.

And we can see that these two angles here are on a straight line.

So the angles on a straight line add up to 180 degrees.

Now again, stick with this for awhile.

We now know that angles on a straight line add up to 180 degrees.

So we have got two angles here on a straight line.

Let's think about what is known and what is not known.

First of all, we know that the angles on the straight line add up to 180 degrees.

And we can represent the whole using a bar model.

So here I can show that 180 degrees represents the whole of the bar model.

The whole is 180 degrees.

In this example, it's split into two parts because we have two angles.

One we know, which is 60 degrees and we can label it on the bar model.

And one we don't know represented here as p.

So let's show that on our bar model.

So expressing this algebraically, and don't be scared by that word because you've been doing algebra since you were in year one and two, we know that 60, which is our known, plus p is equal to 180.

We know that this part equals whole.

Now in order to find the missing part we need to rearrange this so you get the inverse.

So we're going to have a whole 180, take away known part, which is 60, equals unknown part, which is p.

Now I can either do a column subtraction here or I can use my known facts.

I know that 18 take away six is 12.

Therefore I know that 180 take away 60, 120.

Therefore I know that p is equal to 120 degrees and I can check it using the inverse.

So going back to this part, 120 plus 60 should equal to 80 degrees, I mean 180 degrees, sorry, the whole.

There it does, okay? So we have worked our missing part using an algebraic expression.

Now it's your turn.

Pause the video and find the missing angle, a.

Don't forget to draw a bar model to represent the problem.

So you will have drawn a bar model where the whole was 180 degrees split into two parts.

The known was 106 degrees and the unknown part was a.

Algebraically you know that 106 plus a is equal to 180.

Rearranging these in the inverse, 180 subtract 106 is equal to a.

So you probably did a column subtraction here where you regrouped from the 10s.

Okay, so you can see that 180 take away 106 is 74.

So a is equal to 74 degrees.

Good job.

Now on this example the straight line has been split into three angles.

So we're going to approach it in exactly the same way.

We're going to represent using the bar model first.

We know that the value of the whole is 180 degrees.

So we have our bar model, which is split into our three angles and the whole is 180 degrees.

We know one part is 40, so we put it on the bar model.

We don't know the value of the next angle, it's called a, so we label that on our bar model as a.

The third angle hasn't been given to us, but this symbol here lets us know that is a right angle which we know is equal to 90 degrees, so that's on my bar model as well.

So if I express this algebraically I know that with three parts, now part, part, part, whole, I know that 40 plus a plus 90 is equal to 180 degrees.

Now we do this exactly the same way.

We rearrange because we want to get the unknown by itself and we're going to be using the inverse.

180 subtract 40 and 90 is equal to a.

Now you can do this in one of two ways.

Either you can do repeated subtraction, so you can do 180 take away 40 is equal to 140 and then you do 140 take away the 90 which is 50.

Or, so there you know a equals 50.

Or you may challenge yourself to use your knowledge of big math to represent this a different way.

Now you know that if I'm subtracting 40 and then 90 I'm subtracting 40 and 90 all together.

So you could challenge yourself to represent this as 180 take away 40 plus 90 and using your knowledge of big maths you know that whatever is in the brackets must be done first.

So I know that I'm doing 180 take away 40 and 90.

Four plus nine is 13, so 40 plus 90 is 130 and now I know that that is 50.

So it's up to you which strategy you use.

You can either do repeated subtraction or you can represent using big maths, your choice.

So it's your turn.

Now you've got three angles on a straight line.

Don't forget to draw a bar model to represent the problem.

Pause the video now and find the missing angle.

So you will have drawn a bar model where 180, hopefully a neater bar model than me, 180 is the whole.

And this time it was split into three parts.

One part was 46 degrees.

One part was 52 degrees.

And the unknown part was a.

And there we have it much neater.

So algebraically we know that 46 plus 52 plus a is equal to 180.

And reordering it using the inverse, we're doing 180 take away 46 and take away 52 which gave you 82.

So a is equal to 82 degrees.

You may have done repeated subtraction or you may have used big maths.

Now let's start to look at angles around a point.

So let's think back to what we already know.

We worked out that the value of the blue angle is 180 degrees because it was two lots of 90 degrees.

What is the value of the red angle? Well you can see that the red angle is the size as the blue angle, 180 degrees as well.

So both angles together they make a full turn.

So 180 plus 180 is equal to 360 degrees.

So a full turn is equal to 360 degrees.

One full turn is made up of two 180 degree angles or, if I draw this down here, four 90 degree angles.

And we know that four times 90 is also 360.

So let's stick with this.

We know that angles around a point add up to 360 degrees.

So let's think about what is known and what is not known.

First of all, we know that the angles around a point add up to 360 degrees.

And we can represent this using a bar model.

So here we have our whole bar and the whole, the total is 360 degrees.

We know that one angle is 40 degrees, so we can label that one on the smaller part.

And we have an unknown part, which we have called t, and we can add it to our bar model.

So it's the same principle as we've just been practising.

First we represent it pictorially.

Now we go algebraically.

We know that 40 degrees plus t is equal to 360 degrees.

This part equals whole.

Now we rearrange using the inverse so we have whole, 360 degrees, subtract part 40 degrees is equal to part, which is t.

So 360 take away 40 is 320 degrees.

So t is equal to 320 degrees.

And if we just check we know that the whole turn is 360.

So if t is 320 and unknown part was 40 they should add together to make the whole which is 360 degrees.

It's always good to check your answer using the inverse.

Okay, your turn.

Pause the video and find the missing angle.

Draw a bar model to represent the problem.

So you will have drawn a bar model where 360 is the whole.

I think I have one prepared already.

There we go.

So 360's the whole.

And we know one of the parts was 110 and the part that we didn't know was a.

So algebraically 110 degrees plus a is equal to 360 degrees.

Rearranges in the inverse, 360 degrees take away 110 degrees is equal to a.

And we know that 360 take away 110 is 250 degrees.

So a is equal to 250 degrees.

Right, this time we've got something slightly different.

Sometimes you will be given questions where you have two unknowns and in this case you've got to do some detective work.

So here we have f and g are both unknown.

They're not equal, so there must be something else going on.

Now if I look really carefully at this diagram I can see another known part.

There's actually a straight line running through this diagram.

And I know that angles on a straight line add up to 180 degrees.

See this straight line running through? So f can now be worked out by using this angle here, nine.

I know that the whole of this straight line is equal to 180.

And I've been given one part.

180 subtract nine is 171 degrees.

So f is 171 degrees.

Now I can either use that same principle because the bottom part is also on a straight line.

So this is 41 plus g is equal to 180 degrees and then rearrange it, 180 subtract 41 equals g.

That's one way that I could do it.

The other way is to look at the whole diagram as a whole, okay, where 360 is the whole and it's split into four angles.

I know three of them because I worked out f.

41 degrees, nine degrees, and 171 degrees, and now I have to work out g by itself.

So I can use the whole where I know that 360 degrees subtract 41, subtract nine, subtract 171 is equal to g.

And I've done this calculation.

I know that 139 is equal to g.

So g is 139 degrees.

And if you've done it that way we can check it by doing it the other way.

180 subtract 41 is also 139 degrees.

So either way we do it we find g to be 139 degrees.

Okay, now it's time for you to do some independent learning.

Pause the video and complete the task.

Restart the video once you've finished and we'll go through the answers together.

Okay, let's look at question one together.

You have to calculate the value of angle a.

Hopefully you drew a bar model to help to see it and discern it pictorially where the whole is 180 and we subtract the known part which would give us a.

180 subtract 22 is 158.

So a is equal to 158 degrees.

For question two, you were calculating angle c and although it was in a slightly different orientation to what you may be used to seeing, this symbol told us that this angle was 90 degrees.

So the whole is 180 because it's on a straight line.

The known part of 51 and 90 and you're trying to find angle c.

180 subtract 51 and 90 is equal to c.

And I know that 180 subtract 51 subtract 90 is equal to 39 degrees.

So c is equal to 39 degrees.

Question three, we're looking at a full turn.

So you know that one full turn is equal to 360 degrees.

Whole subtract part equals part.

360 subtract 78 is 282 degrees.

So b is equal to 282 degrees.

Question four, you're calculating angle f.

The whole, again, is around a full turn or 360.

And there are your two known parts and your missing part.

So whole 360, subtract part 165, subtract part 68, is equal to f.

And I know that this is 127 degrees.

So f is equal to 127 degrees.

Question five we've got two unknown angles and we can this straight line running all the way through.

So I have two bar models to help me.

I'll start out with f and I've got one known which is 45 degrees.

So 180 subtract the known 45 degrees is equal to 135 degrees.

So f is equal to 135 degrees.

And then g is my other unknown.

And I know that I'm doing a whole 180 subtract 85 here which is equal to 95.

So g is equal to 95 degrees.

Okay, now it's time to pause the video and complete your final quiz.

Restart the video once you're finished.

In our next lesson, we'll be learning to compare and classify triangles.

See you then!.