Why do all exterior angles on a polygon add up to 360 when the interior changes depending on sides?

Question

Why do all exterior angles on a polygon add up to 360 when the interior changes depending on sides?

In: 6

Answer 1

The total angles at every vertex of the polygon add up to 180. They have to, since the interior and exterior angles form a straight line by definition. So the sum of both interior and exterior angles of a polygon with *n* vertices is necessarily 180 * n

The interior angles add up to 180(n-2), or if you prefer, 180n – 360 (just distribute the 180 into the parentheses). So the remaining 360 have to go to the exterior angles.