A polygon of n sides has 90 diagonals, then n is equal to

Step-by-step solution

The formula for number of diagonals in a polygon of n sides is D = n(n-3) 2 Setting D = 90 : n(n-3) 2 = 90 n^2 - 3n - 180 = 0 (n-15)(n+12) = 0 n = 15 or n = -12 Since n must be a positive integer, n = 15 .