Lesson video

In this lesson, we're going to be finding the sum of the interior angles of a polygon.

To find the sum of the interior angles of a polygon, we're going to start by splitting the polygon into the minimum number of triangles.

In this example, our pentagon can be split into a minimum of three triangles.

We know that each triangle has 180 degrees in it.

To find the sum of the interior angles of a polygon, we multiply the minimum number of triangles by 180 degrees.

In this case, to find the sum of interior angles in a pentagon, we're multiplying 180 by three, which gives us 540 degrees.

The sum of the interior angles in a pentagon is 540 degrees.

Here are some questions for you to try.

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

Here are the answers.

To find the minimum number of triangles that a polygon can be split into, you need to subtract two from the number of sides.

To then find the sum of the interior angles, you multiply the number of triangles by 180.

Here is a question for you to try.

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

Here is the answer.

There should only be 14 triangles drawn in this polygon.

Nick needs to make sure that you sign in the minimum number of triangles.

We've worked out that the sum of the interior angles in a pentagon is 540 degrees.

With this example, we're finding the missing angle, labelled a.

All five of the angles in this pentagon need to add to 540 degrees.

Let's start by adding the four angles that we've been given.

These sum to 477.

To find the size of angle a, we're going to subtract this from 540.

This gives us an answer of 63 degrees.

Here are some questions for you to try.

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

Here are the answers.

You needed to work out the sum of the interior angles of each polygon first.

You could have used your table from question one to do this.

In part d, you needed to find the reflex angle within the polygon, and then use that to find angle x.

Here are some questions for you to try.

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

Here are the answers.

To find the number of triangles, we can write it as n minus two.

To find the sum of interior angles, this could be written as n minus two multiplied by 180.

Make sure the n minus two is in brackets.

In question six, the sum of interior angles of a hexagon is 720.

Because it is a regular hexagon, this means that all of the angles are equal.

So to find one of them, we do 720 divided by six, which is 120 degree.

That's all for this lesson.

Thanks for watching.