Question

How many sides does a regular polygon have, whose interior angle is eight times its exterior angle?

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

Answer 1

Answer: (C)

$18$

Interior angle of a regular polygon of '$n$' sides $=\frac{(n-2)\times {180}^{\circ }}{n}$
Exterior angle of a regular polygonof '$n$' sides
Given, $\frac{(n-2)\times {180}^{\circ }}{n}=8\times \frac{{360}^{\circ }}{n}$
$\Rightarrow (n-2)=8\times \frac{{360}^{\circ }}{{180}^{\circ }}=16$

$\Rightarrow n=18$