Question

Hiw many diagonal of different lengths are possible in a convex regular decagon

Answer 1

Times 10 equals 70; each diagonal is counted twice, so the final answer is 35. Now, using combinations and such: There are ("10 choose 2") pairs of vertices, which equals 45. So there are 45 line segments joining pairs of vertices. Exactly 10 of those are sides of the decagon, the others are diagonals.