Lesson video

Welcome to our fourth lesson in this unit, finding missing angles and length.

Today we're going to be finding the value of missing angles in triangles.

All you'll need is a pencil and a piece of paper.

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

Here's our agenda.

So we'll be finding the value of missing angles in triangles today, starting with a quiz to test your knowledge from yesterday's lesson, then we'll represent angles pictorially, we'll calculate missing angles before you do some independent work and a final quiz.

So let's start with the knowledge quiz.

Pause the video to complete the quiz, and test your knowledge from yesterday's lesson.

Great work, now we're looking today at the angles in a triangle.

We know that the angles in a triangle add up to 180 degrees.

In an equilateral triangle, where all of the sides are equal, the angles are always 60 degrees each.

In an isosceles triangle where two of the sides are equal length, two of the angles are equal, and one is different.

In a scalene triangle all of the angles are different sizes.

Now we can represent the angles in a bar model pictorially.

So the whole is 180 degrees.

And the three angles added together total 180 degrees.

As an algebraic expression we can represent that as a plus b, plus c equals to 180 degrees.

In this case, as it's a scalene triangle angles a, b and c are all different.

But what about in an isosceles triangle? What do we know about angles b and c? We know that angles b and c are equal.

And we know that a is different and it looks smaller than b and c as well.

So we can represent it using a bar model.

Again a whole is 180.

We've got our missing angle a which is different to the other two, and b and c are equal.

So their bars are the same length.

And then we know that a plus b plus c equals to 180 degrees, but in this case, b is equal to c, and we'll look at how we work with that with using actual numbers in a minute.

Now it's your turn.

Represent the equilateral triangle pictorially, and then algebraically.

So you will have drawn a bar model with a whole as 180 degrees, and you have three bars of equal length.

Algebraically a plus b plus c is equal to 180 degrees.

And as it's an equilateral triangle, we know that a is equal to b which is equal to c.

Now let's get on with calculating some missing angles.

Here we have a scalene triangle where all of the angles are different.

We want to know the value of angle a.

Let's represent as always pictorially first, but we have our whole is 180 degrees, and we have two known angles, 30 degrees and 135 degrees.

And our unknown angle is angle a.

Represented algebraically we can see that 30 degrees plus 135 degrees plus a is equal to 180 degrees.

Now in order to find the missing part, which is a, we need to rearrange the equation using the inverse.

So we had part, plus part, press part equals whole.

Now whole take away part, takeaway part is equal to part, the unknown part.

Now we touched on this in the previous lesson, we have two ways of doing this.

Either we can use repeated subtraction, or you may represent it using BIDMAS.

So I'll start off with repeated subtraction.

So 180 subtract 135.

Regroup from my tens.

So that's 45, and then I'm doing 45 subtract 30.

So I can see that a is equal to 15 degrees.

Now, if you were representing using BIDMAS, you would know that when I'm doing 180 takeaway 135, takeaway 30, what I'm doing is 180 takeaway both of these numbers together.

I may have shown it like this 180 takeaway 135 and 30.

And my brackets tell me to do this first.

So you're doing 180 away 165, which is equal to 15 degrees.

So it's your choice, how you do it.

But in fact, sometimes this is the most efficient way to do it because you're really doing a step less than in the other strategy.

Now it's your turn.

Pause the video and represent the angles pictorially and algebraically to find the value of the missing angle, we call it a.

So your bar model will look like this, 180 degrees is the whole.

You knew this angle, although it wasn't written on there because you know the symbol, 90 and 70, with my degree sign in there, and a equal to 180.

Algebraically, we know that 90 plus 70 plus a is equal to 180 and that needed rearranging.

So you had to use your knowledge of the inverse to rearrange that to 180, subtract 90, subtract 70, is equal to a, or you may have done your brackets to do it using BIDMAS, 180 takeaway 90 and 70.

And I can do this in my head.

I know that nine and seven is 16.

So 90 and 70 is 160.

So a is equal to 20 degrees.

Now we're going to calculate the missing angles in an isosceles triangle.

We know that in this triangle angles b and c are equal, and we haven't been given the size of either of those angles.

So fast here is our bar model.

The whole is 180 degrees.

The known is 32.

B and c are the same size angle.

B is equal to c.

So we know that we're subtracting 32 from 180 to give us the value of b and c together.

So I know that's 148, because that's 180 take away 32 is equal to b and c.

So I know that b and c are equal to 148, and because they are equal, I need to divide 148 by two to find their value.

So the value of b and c is 74 degrees each.

Now it's your turn.

Here's another isosceles triangle.

Pause the video and represent the angles pictorially and algebraically to find the value of the missing angles a and b.

So for this one, you will have drawn your bar model with your known 110 and your unknowns, a and b, where a is equal to b.

So you know that 180 subtract your known angle gives you what is left over is a and b and that's 70 degrees.

So now you know that this 70 needed to be split equally between don't know, sorry, why I've changed this to b and c there.

That should be a and b, cause a and b equal 70 degrees altogether, and 70 divided by two is 35 degrees.

Remember that you can always check your answer using the inverse.

So you're adding 110, 35 and 35 that should equal to 180.

110 plus 35 is 145.

Plus another 35 is 180.

So I can check by going the opposite way to check that it still works.

Now you're going to do another one.

This is another isosceles triangle, represent it pictorially, and then algebraically to find the value of angle a.

So in this one, we didn't know this angle.

It just wasn't written on for you.

You know that the whole is 180.

The two known parts are 40 and 40.

So subtracting those two from 180 is the answer to a.

So a in this case is equal to 100 degrees.

Remember the angles in a triangle add up to 180, so you can check it.

100 plus 40 is 140, plus another 40 is 180.

So that's definitely correct.

Now it's time for your independent learning.

Pause the video and complete the tasks, and then restart once you're finished.

Okay, here's your first question.

Question one, you're asked to calculate the value of angle a in this scalene triangle.

Here's your pictorial representation.

The whole is 180.

The two known parts are here.

So you will write it algebraically.

180 takeaway 48, takeaway 62 equals a, or you may have used BIDMAS, 180 takeaway 48 plus 62.

And you will have found that a is equal to 70 degrees.

Question two your isosceles triangle.

We know the two parts, 63 degrees.

The missing part was a, so we're doing 180 takeaway 63, takeaway 63 equals a, or you may have done 180 take away 63 plus 63, even 63 times two.

And you will have found that a was equal to 54 degrees.

for question three you had a right angled triangle.

So this one was 90 degrees.

You know, I've got my letters all muddled up here.

The angle was y here.

So in fact, I'll change it to either.

So you know that algebraically 180 takeaway 37, takeaway 90 is equal to a, and again you may have done that using BIDMAS to find that a is equal to 53 degrees.

Question four, you have an isosceles with the two equal angles are unknown.

So you know that 180 take away 32 is equal to a and b together.

180 takeaway 32 is 148.

So a and b together 148 degrees, because they're equal we have to divide 148 by two, which gives us 74 degrees.

So both a and b are equal to 74 degrees.

In question five you were asked to calculate the angles y and z.

And I gave you a hint, start off by finding angle z.

Now you can see the angles z is on a straight line with 130.

We know that the angles on a straight line add it to 180.

So 180 subtract 130 equals z.

180 subtract 130 is 50 degrees.

So now we're just looking at a triangle where we have two known parts and one unknown.

So you're doing 180 takeaway 75 and 50, will give you y and that is equal to 55 degrees.

Great work, now it's time for your final quiz.

Pause the video and complete the quiz.

Great work today.

In our next lesson we'll be finding the value of missing angles in quadrilaterals.

I'll see you then.