Question

Is it possible to have a regular polygon whose each interior angle is ${150}^{\circ }$

• A. No
• B. Yes
• C. Cannot be determined
• D. None of these

Answer 1

The correct option is B Yes

Each interior angle of regular polygon of n sides is given by $\frac{180(n-2)}{n}$ degree

$\frac{180(n-2)}{n}={150}^0$

$\Rightarrow 180(n-2)=150n$
$\Rightarrow 180n-360=150n$
$\Rightarrow 30n=360$
$\Rightarrow n=12$
${\text{Clearly, there is a polygon of sides 12 whose each interior angle is 150}}^o.$