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

1 Answer
Cesareo R.
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#

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