Question

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

Answer 1

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`