Exterior Angles of Polygons

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

Straight line showing interior and exterior angles adding to 180 degrees

More examples:

Triangle with one side extended to show the exterior angle

Polygon side extension showing the exterior angle relationship at a different orientation

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

Exterior Angle + Interior Angle = 180°

Polygons

A Polygon is any flat shape with straight sides

The exterior angles of a polygon add up to 360°

images/exterior-angles.js

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.

Irregular polygon with all exterior angles marked to show a full rotation

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

830,831, 1776,832, 1777, 3317, 3318, 3319, 7491, 9062