The sum of the interior angles of a regular polygon is six times the sum of its exterior angles. Determine the number of diagonals in the polygon.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 77.
Sum of interior angles of n-sided polygon = (n – 2) × 180
⇒ (n – 2) × 180 = 6 × 360 = 2160
⇒ n – 2 = 2160/180 = 12
⇒ n = 14
Number of diagonals = [n(n – 3)]/2 = [14(14 – 3)]/2 = [14 × 11]/2 = 77