How many sides are there in a polygon which has 20 diagonals?

Step-by-step solution

The number of diagonals of an n -sided polygon is given by ^ n C₂ - n = n(n-3) 2 . Given that the number of diagonals is 20 . n(n-3) 2 = 20 n^2 - 3n - 40 = 0 (n-8)(n+5) = 0 Since the number of sides n must be a positive integer, n = 8 . Answer: 8