What is the sum of a convex polygons exterior angles?

Answer 1

Remember that the internal angle of a regular convex polygon is (n - 2) * 180 degrees / n, where n is the number of sides in the polygon.

Also remember that the external angle of a regular convex polygon is 180 degrees minus the internal angle a polygon.

So the external angle of a polygon is 180 - ((n - 2) * 180 / n). The sum of the angles will be the external angle multiplied by n, or:

(180 - ((n - 2) * 180) / n ) * n =

180 * n - (n - 2) * 180

Please note that I only proved this for regular polygons, but this formula should also extend to irregular convex polygons too. If a teacher asks you for a proof, then this will be insufficient.