Polygons: Sum of Exterior Angles

The exterior angles of a triangle, quadrilateral, and pentagon are shown, respectively, in the applets below. Control the size of a colored exterior angle by using the slider with matching color. Move the vertices of these polygons anywhere you'd like. For the quadrilateral & pentagon, the last two applets work best if these polygons are kept convex. If you don't remember what this term means, click here for a refresher.

Exterior Angles of a Triangle

Exterior Angles of a Quadrilateral

Exterior Angles of a Pentagon


What do you notice? What is common about the measures of the exterior angles of any one of these polygons?


Do you think what you've observed for the triangle, quadrilateral, and pentagon above will also hold true for a hexagon, heptagon, and octagon? Make a conjecture about the sum of exterior angles of a convex polygon: