Regular polygon exterior angle 50, how many sides

Step by step

The question

Question: find how many sides a regular polygon has, when its exterior angle is 50°.

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 Count the turns

Each turn is 50°.

How many turns of 50° make 360°?

360/50.

360 divided by 50 is 7.2.

A shape cannot have 7.2 sides.

So no regular polygon has an exterior angle of 50°.

It is impossible.

Let's look back.

First: walk around the shape.

Last: count the turns.