A polygon has 1325 diagonals. How many vertices does it have?

Answer: it has 53 vertices.

Explanation:

If a polygon has N vertices, then every vertex has (N-3) vertices that are nonadjacent, with a diagonal between them. Since every diagonal connects 2 vertices, division by 2 will avoid counting diagonals twice.

If N(N-3)/2 = 1325,

then N=53
Edited on February 1, 2004, 10:08 am

Posted by Penny on 2004-01-31 10:43:08