Question

Is it possible to have a regular polygon whose each interior angle is ${145}^{\circ }$

• A. No
• B. Yes
• C. May be
• D. Cannot be determined

Answer 1

The correct option is A No

Each interior angle of regular polygon of n sides is given by $\frac{180(n-2)}{n}$
$\frac{180(n-2)}{n}={145}^0$
$\Rightarrow 180(n-2)=145n$
$\Rightarrow 180n-360=145n$
$\Rightarrow 35n=360$
$\Rightarrow n=\frac{72}{7}$
$\text{Which is not possible because number of sides can never be in fraction.}$