The sum of all interior angles of a regular polygon is 1080°. How many diagonals does the polygon have?
Show answer & explanation
Correct answer: A
Explanation
Sum of interior angles = 1080°
According to the formula:
(n − 2) × 180 = Sum of interior angles
Number of diagonals = n(n − 3) / 2
(n − 2) × 180 = 1080
n − 2 = 6
n = 8
Diagonals = 8(8 − 3) / 2 = 20