Correct Answer - Option 3 : 54
Given:
Difference between exterior and interior angle a polygon is 120° (interior angle > exterior angle).
Formula Used:
1. Each exterior angle of the polygon = 180° - Each interior angle of the polygon
2. Number of diagonals of regular polygon = [n (n – 3)] / 2
3. An exterior angle of polygon = 360°/n
Where n = number of sides.
Calculation:
Let, the interior angle is x and exterior angle is y
Accordingly,
x - y = 120° ----(1)
x + y = 180° ----(2)
From (1) and (2) get,
y = 30° and x = 150°
The exterior of the given polygon is 30°
The number of sides of the polygon
= 360°/30° = 12
Number of diagonals of the polygon is {12 × (12 – 3)}/2
⇒ (12 × 9)/2 = 54
∴ The number of diagonals of the polygon is 54
