Regular polygon interior angle 108, how many sides

Step by step

The question

Question: find how many sides a regular polygon has, when its interior angle is 108°.

1 Find the exterior angle

The interior angle is 108°.

The exterior angle sits next to it.

Together they make a straight line: 180°.

So the exterior angle is 180 − 108.

Careful: the 360° is for the exterior angles.

So we need the exterior angle first.

180 minus 108 is 72°.

2 Walk around the shape

Walk along the edge.

At a corner, carry the side on, dashed.

Then turn to the next side.

The turn is the exterior angle.

All the way round, we end up facing the same way as at the start.

That is one full turn.

So the exterior angles add up to 360°.

A regular shape turns the same at every corner.

3 Count the turns

Each turn is 72°.

How many turns of 72° make 360°?

360/72.

360 divided by 72 is 5.

So 5 turns: 5 corners and 5 sides.

Here is the whole shape: 5 sides.

4 Check

Let's check: 5 turns of 72°.

We get 360°, one full turn.

So 5 sides is right!

Let's look back.

First: find the exterior angle.

Then: walk around the shape.

Then: count the turns.

Last: check.