Question : Find the number of diagonals of a regular polygon, whose sum of interior angles is 2700°.
Option 1: 121
Option 2: 119
Option 3: 127
Option 4: 117
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Correct Answer: 119
Solution : Let's denote the number of sides of the regular polygon as n. The sum of interior angles = (n – 2) × 180° ⇒ 2700 = (n – 2) × 180° ⇒ n = 15 + 2 $\therefore$ n = 17 Number of diagonals of a polygon $=\frac{n × (n - 3)}{ 2}=\frac{17×14}{2}=119$ Hence, the correct answer is 119.
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