Exterior angle of a regular decagon

Step by step

The question

Question: find one exterior angle of a regular decagon.

1 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.

We turn at every corner.

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.

2 Share it out

10 equal turns make 360°.

So we share it: 360/10.

360 divided by 10 is 36.

So each exterior angle is 36°.

3 Check

Let's check: 10 turns of 36° together.

We get 360°, one full turn.

So 36° is right!

Let's look back.

First: walk around the shape.

Then: share it out.

Last: check.