Sum of the Exterior Angles of a Polygon

An external, or exterior, angle is the one that is found between an original side of the polygon and its extension.

The angle is located outside of the polygon and hence its name derives.

Observe only the original sides of the polygon.

Now imagine that, the person who was drawing the polygon fell asleep while doing it, without realizing it they continued outlining one of its sides a little more.

The angle that is created between the original side and the side that was unintentionally continued, is the external angle.

The sum of the external angles of a polygon will always be $360^o$ degrees! In any polygon that is.

Observe, the exterior angle is located between the side that was extended by "falling asleep" and the original side of the polygon.

An angle originated between two sides that were extended by "falling asleep" is not considered an external angle.