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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