Question

In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

• A. 30
• B. 54
• C. 64
• D. None of Above

Answer 1

The Correct Option is B

A polygon with 'n' sides can be expressed as having an inner angle sum of \((2n−4)× 90\) and an external angle sum of 360 degrees. 
Consequently, \(120\times n\) 
\(⇒ (2n−4)90−360=120n \)
\(⇒ 60n = 720 \)
\(⇒ n = 12\) will be the difference between them. 
We are aware that a regular polygon has \(^nC_2 - n = ^{12}C_2 - 12 = 66 - 12 = 54\) diagonals. 
The correct answer is (B): 54.