If a regular polygon has 35 diagonals, what is the measure of each of its interior angles?
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Correct answer: A
Explanation
Number of diagonals = 35
Diagonals = n(n − 3) / 2
Interior angle = [(n − 2) × 180] / n
n(n − 3) / 2 = 35
n(n − 3) = 70
n² − 3n − 70 = 0
(n − 10)(n + 7) = 0
n = 10
Interior angle = [(10 − 2) × 180] / 10 = 144