Question

Find the number of sides in a regular polygon if each exterior angle is ${\left[22\frac{1}{2}\right]}^{\circ }$.

• A. $16$
• B. $15$
• C. $8$
• D. $10$

Answer 1

The correct option is A $16$

$\text{Each exterior angle of regular polygon of n sides is given by}\frac{360}{n}degree$
$\text{According to question}$
${\frac{360}{n}}^o={\frac{45}{2}}^o$
$\Rightarrow n=\frac{2}{45}\times 360$
$\Rightarrow n=16$
$\therefore \text{Number of sides =16}$