If a polygon of n sides has 560 diagonals, then n =

Step-by-step solution

The number of segments obtained by joining n vertices of a n -sided polygon will be C 2 n out of which n will be the sides of the polygon. So, the number of diagonals will be C 2 n - n . i.e. C 2 n - n = 560 ⇒ n n - 1 2 - n = 560 ⇒ n 2 - 3 n - 1120 = 0 ⇒ n + 32 n - 35 = 0 Hence, n = 35