The exterior angle of a polygon

The exterior angle at a vertex (corner) of a shape is made by extending a side.

Exterior angles of a polygon diagram

Sum of exterior angles

The exterior angles of a polygon add up to 360^\circ.

Imagine walking round the outside of the polygon. By the time you get back to where you started you have completed one full turn. So all the corners you turned must add to 360^\circ.

In this diagram the exterior angles have been given different colours. You can see how they can be put together to make a full circle.

Sum of exterior angles of a polygon