Exterior Angles of Polygons

The Exterior Angle is the angle between any side of a shape,
and a line extended from the next side.

interior exterior angles

Another example:

interior exterior angles

When we add up the Interior Angle and Exterior Angle we get a straight line 180°. They are "Supplementary Angles".


A Polygon is any flat shape with straight sides

The Exterior Angles of a Polygon add up to 360°


In other words the exterior angles add up to one full revolution.

Press Play button to see.

(Exercise: try this with a square, then with some interesting polygon you invent yourself.)

Note: This rule only works for simple polygons.

Here is another way to think about it:
Each lines changes direction until we eventually get back to the start:
exterior angles polygon