How many diagonals does a polygon with 24 sides have?

First, consider that there are 24 vertices for diagonals to come from, and they each have 21 places to go, since they can’t go to themselves, or to the adjacent vertices. (24)(21) therefore equals twice the number of diagonals, since I just counted each one twice (once per endpoint). There are therefore (24)(21)/2 = 252 diagonals.