What is the sum of the exterior angle measures for an irregular convex octagon?

1 Answer
May 29, 2016

The sum of the exterior angle measures for an irregular convex polygon is 2pi

Explanation:

For any convex polygon the sum of internal angles is given by the number of different triangles with which can be decomposed. Then a polygon with n sides has a net sum of internal angles given by
(n-2)pi. For each angular vertex the complement to the internal angle assigned the correspondent internal angle, angle "internal"_i sums as an external angle. The complementary angle is given by pi - angle "internal"_i and we have
"external sum" = sum_i^n (pi-angle "internal"_i) = n pi - (n-2)pi = 2pi