If the sum of the interior angles of a regular polygon is 2520°, determine the number of sides and the total number of diagonals of the polygon.
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Correct answer: A
Explanation
Sum of interior angles = 2520°
Sum of interior angles = (n − 2) × 180
Number of diagonals = n(n − 3) / 2
(n − 2) × 180 = 2520
⇒ n − 2 = 14
⇒ n = 16
Number of diagonals = 16(16 − 3) / 2 = 104
16 sides, 104 diagonals