Question

The interior angle of a regular polygon exceeds the exterior angle by \(132^\circ\). Then the number of sides in the polygon is

Answer 1

Correct Answer: 1

Concept:

• Interior + Exterior angle = \(180^\circ\)
• Exterior angle of regular polygon = \(\frac{360^\circ}{n}\)

Step 1: Form equation.
Let exterior angle = \(x\) \[ \text{Interior} = 180 - x \] Given: \[ (180 - x) - x = 132 \]
Step 2: Solve.
\[ 180 - 2x = 132 \Rightarrow 2x = 48 \Rightarrow x = 24^\circ \]
Step 3: Find number of sides.
\[ \frac{360}{n} = 24 \Rightarrow n = \frac{360}{24} = 15 \]
Step 4: Option analysis.

• (A) 15: Correct \checkmark
• (B) Incorrect $\times$
• (C) Incorrect $\times$
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (A).