Question

Find the number of sides in a regular polygon, if each interior angle is ${160}^{\circ }$

• A. $16$
• B. $20$
• C. $14$
• D. $18$

Answer 1

Answer: (D)

$18$

$\text{Each interior angle of regular polygon of n sides is given by}\frac{180(n-2)}{n}$ degree
$\text{According to question}$
${\frac{180(n-2)}{n}}^o={160}^0$
$\Rightarrow 180(n-2)=160n$
$\Rightarrow 180n-360=160n$
$\Rightarrow 20n=360$
$\Rightarrow n=18$
$\therefore \text{Number of sides =18}$