A regular polygon of n sides has 170 diagonals, then n is equal to

Step-by-step solution

The number of diagonals in a polygon with n sides is given by the formula D = n(n-3) 2 . Given that the number of diagonals is 170, we set up the equation: n(n-3) 2 = 170 n(n-3) = 340 n^2 - 3n - 340 = 0 To solve this quadratic equation, we find factors of -340 that sum to -3. These are -20 and 17. (n - 20)(n + 17) = 0 This gives n = 20 or n = -17 . Since the number of sides n must be a positive integer, we have n = 20 . Answer: 20