Question

How many sides does a regular polygon have with its interior angle as eight times its exterior angle.

• A. $16$
• B. $24$
• C. $18$
• D. $20$

Answer 1

The correct option is C $18$

For a $n$-sided regular polygon
Each interior angle $=\frac{(n-2)\times {180}^o}{n}$
Each exterior angle $=\frac{{360}^o}{n}$
Given, $\frac{(n-2)\times {180}^o}{n}=8\times \frac{{360}^o}{n}$
$\Rightarrow$ $n-2=16$ $\Rightarrow$ $n=18$