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 (N3) 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(N3)/2 = 1325,
then N=53
Edited on February 1, 2004, 10:08 am

Posted by Penny
on 20040131 10:43:08 