Question

Find the number of sides in a regular polygon, if its each interior angle is ${135}^{\circ }$.

• A. $2$
• B. $9$
• C. $8$
• D. $6$

Answer 1

The correct option is C $8$

Each interior angle of regular polygon of $n$ sides is given by ${\frac{180(n-2)}{n}}^o$
According to question, ${\frac{180(n-2)}{n}}^o={135}^0$
$\Rightarrow 180(n-2)=135n$
$\Rightarrow 180n-360=135n$
$\Rightarrow 45n=360$
$\Rightarrow n=8$
$\therefore \text{Number of sides =8}$