Exterior Angles of Polygons

An exterior angle is the angle between one side of a shape and a line extended from the next side.

More examples:

When we add up the interior angle and its matching exterior angle we get a straight angle 180°, so they are supplementary angles.

Polygons

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.

We can also think "each line changes direction
until we get back to the start again":

Imagine walking all the way around a park along straight paths:

At each corner, you turn by the exterior angle. When you get back to your starting point you have made one full turn of 360°.

Regular Polygons

In a regular polygon, all sides and all angles are equal. That means all exterior angles are equal, too!