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 $=\frac{(n-2)\times {180}^{\circ }}{n}$
$\Rightarrow {150}^{\circ }=\frac{(n-2)\times {180}^{\circ }}{n}$
$\Rightarrow 150n=(n-2)\times {180}^{\circ }$
$\Rightarrow 180n-150n=360$
$\Rightarrow 30n=360$
$n=\frac{360}{30}$
$n=12$

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