Lesson video

Hello, my name is Mr Clasper.

And today we're going to be finding missing exterior angles.

In this lesson, we're going to be looking at exterior angles.

But it's important to be able to identify both exterior angles and interior angles.

In the diagram, we have a hexagon.

Within the hexagon, we have six interior angles.

These are known as interior angles as they reside on the inside of this polygon.

So interior angles are inside any polygon.

An exterior angle compliments, an interior angle to create a straight line.

So this is an exterior angle, which resides on the outside of a polygon.

And again, as the interior and exterior angles are on a straight line, they have a sum of 180 degrees.

Here's a question for you to try.

Pause the video to complete your task and click resume once you're finished.

And here are the solutions.

So remember exterior angles are on the outside of any polygon.

And interior angles reside inside the polygon.

Let's take a look at this diagram.

This is a diagram of an equilateral triangle.

In an equilateral triangle, we have three equal angles and they must have a sum of 180 degrees.

Therefore, each of the interior angles of this equilateral triangle, must be 60 degrees.

We also have three exterior angles located here.

And thinking about the relationship between our interior and exterior angles, as these must have a sum of 180 degrees, that means each of my exterior angles must be 120 degrees.

If we look at our three exterior angles, they have a sum of 360 degrees.

Let's have a look at this example.

This square has four, 90 degree interior angles.

The square also has four, 90 degree exterior angles.

And again, the sum of my exterior angles is 360 degrees.

In any polygon, the sum of my exterior angles will always be equal to 360 degrees.

Let's have a look at this example.

We need to calculate the size of angle a.

We've been given three exterior angles.

However, we know that these three exterior angles must have a sum of 360 degrees.

Therefore, we know that when we add all three of these angles together, they have a sum of 360 degrees.

If I tied this equation up, I get 215 degrees plus a must be equal to 360 degrees.

And if I subtract 215, from 360, I get a value of 145 degrees for the size of a.

Here's some questions for you to try.

Pause the video to complete your task and click resume once you're finished.

And here are your solutions.

So again, the fact that we're going to use is that the sum of exterior angles of any polygon must be 360 degrees.

So if we subtract 150 and 100 from 360, we get our first solution of 110 degrees for the size of angle a.

And likewise, for the second example, we have five angles, one of which we don't know, but we know that all five of these have a sum of 360 degrees, which should lead us to the conclusion that b is equal to 85 degrees.

Here's a question for you to try.

Pause the video to complete your task and click resume once you're finished.

And here are the solutions.

So if we think about this carefully, a regular polygon must have equal sides and equal interior angles, and it also has equal exterior angles.

So if we have three equal angles, that must have a sum 360.

If I share 360 into three equal pieces, that means that each exterior angle must be 120.

And if I continue down that path, I can calculate 360 divided by four to get my 90 degree angle for a square.

If I calculate 360 divided by five, I get an exterior angle of 72 degrees for a pentagon.

And if I calculate 360 divided by six, I get an exterior angle of 60 degrees on a hexagon.

Let's take a look at this example, we're asked to find the value of a, given the three exterior angles.

However, this time the three exterior angles are given as expressions in terms of a.

We can still apply what we know in that these three exterior angles must have a sum of 360 degrees.

So if we add all three exterior angles together, they must equal 360.

If I simplify my expression on the left-hand side, this would leave me with nine a plus 180, and this still must equal 360.

Subtracting 180 from both sides would mean that nine a must be equal to 180.

And dividing both sides of my equation by nine, means that the value of a must be equal to 20.

Here's your last question.

Pause the video to complete your task and click resume once you're finished.

And this is the solution for our final problem.

So for part a, we are asked to form and solve an equation to find the value of X.

So our equation would be found by adding each of my five exterior angles together.

So if I add these together, I should end up with an equation of 10 X plus 210 must be equal to 360.

Part b, We need to find the size of the largest angle.

So what I would do first is to solve our equation from part a, so when you solve that, you should find that the value of X is actually 15.

And from there, if we substitute 15 into each of the five expressions for our angles, we can find the size of the smallest angle.

So the smallest angle is 110 degrees.

And that is the end of our lesson.

So now you can find missing exterior angles, that's fantastic.

Why not try our exit quiz just to boost your confidence further? I'll hopefully see you soon.