Question

What is the sum of the angle measures of a 36-gon?

Answer 1

The general formula for a n-gon would be (n-2)x180.
Take a vertex and name it A. Now, you can draw diagonals to each and every other vertex from the 36-gon, except himself, and two which form a side with A. In total you can draw 33 lines. When you look at it, you formed 34 triangles, so,. the sum of the angles of your 36-gon is the sum of the angles of 34 triangles. Since the sum of the angles measures of a triangle is 180º, then the answer you are looking for is 34x180º = 6120º.