Question

How many sides does a regular polygon have if each of its interior angles is ${165}^o$?

• A. $24$
• B. $26$
• C. $16$
• D. $18$

Answer 1

Answer: (A)

$24$

Let there be n sides of the polygon. Then, its each interior angle $=\left(\frac{(n-2)\times {180}^o}{n}\right)$
$\therefore \frac{n-2}{n}\times 180=165$
$\Rightarrow 180n-360=165n$
$\Rightarrow 180n-165n=360$
$\Rightarrow 15n=360$
$\Rightarrow n=\frac{360}{15}=24$
Thus, there are 24 sides of the polygon.