Question

Find the number of sides in a regular polygon, if its each interior angle is $1\frac{1}{5}$ of a right angle.

• A. $6$
• B. $2$
• C. $3$
• D. $5$

Answer 1

The correct option is D $5$

Each interior angle of regular polygon of $n$ sides is given by ${\frac{180(n-2)}{n}}^o$
$\therefore \frac{180(n-2)}{n}=\frac{6}{5}\left({90}^0\right)$
$\Rightarrow 900(n-2)=540n$
$\Rightarrow 5(n-2)=3n$
$\Rightarrow 5n-10=3n$
$\Rightarrow 2n=10$
$\Rightarrow n=5$
$\therefore \text{Number of sides =5}$