The sum of the interior angles of a polygon of ' n ' sides is given by (2n−4)×90, and the sum of the exterior angles of a polygon is 360 degrees. So, the difference between them will be 120‌*n ‌⇒(2n−4)90−360=120n ‌⇒60n=720⇒n=12 We know that the number of diagonals of a regular polygon is nC‌2‌n=12C2−12=66−12=54.