If in a regular polygon the number of diagonals is 54 , then the number of sides of this polygon is:

Step-by-step solution

Number of diagonals of an ′ n ′ sided polygon is   n C 2 - n = 54 n n - 1 1.2 - n = 54 n 2 - n 2 - n = 54 n 2   - 3 n   =   108 n 2 - 3 n - 108 = 0 n - 12 n + 9 = 0 n = 12