Question

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

• A. $24$
• B. $44$
• C. $55$
• D. $33$

Answer 1

The correct option is A $24$

$\Rightarrow$ Interior angle of given polygon $={165}^o$

$\Rightarrow$ Exterior angle of polygon $={180}^o-{165}^o={15}^o$

$\Rightarrow$ The sum of exterior angles of any polygon is ${360}^o$

$\Rightarrow$ Number of sides of regular polygon $=\frac{{360}^o}{{15}^o}=24$