Question

Find the number of sides in a regular polygon if its each interior angle is:​(ii) ${150}^{\circ }$.

Answer 1

Let the number of sides be $n$.
Given : Each interior angle $={150}^{\circ }$

We know that , each interior angle $=\frac{(n-2)\times {180}^{\circ }}{n}$

$\therefore$ $150=\frac{(n-2)\times {180}^{\circ }}{n}$

$\Rightarrow$ $150n=(n-2)\times 180$

$=180n-360$

$30n=360$

$n=\frac{360}{30}$

$\therefore$ $n=12$

Hence, the required number of sides is $12$.