Question

Find the number of sides in a polygon whose each interior angle measures ${140}^o$.

• A. $6$
• B. $7$
• C. $8$
• D. $9$
• E. $10$

Answer 1

The correct option is D $9$

Sum of angle in polygon is=$(n-2)\times {180}^{\circ }$, where $n$ is the number of sides

$\therefore$ Each angle is $\frac{(n-2)\times {180}^{\circ }}{n}$

As given each interior angle is${140}^{\circ }$ so

$\Rightarrow 140=\frac{(n-2)\times 180}{2}$

$\Rightarrow 140n=180n-360$

$\Rightarrow 140n-180n=360$

$\Rightarrow 40n=360$

$\Rightarrow n=\frac{360}{40}=9$