Question

There is a regular polygon whose each interior angle is ${145}^{\circ }$
State true or false.

• A. True
• B. False

Answer 1

The correct option is B False

Given, a polygon whose each interior angles is ${145}^o$
Sum of interior angles of a polygon is = ${180}^o(n-2)$
Each interior angle of a polygon = $\frac{{180}^o(n-2)}{n}$
$\frac{{180}^o(n-2)}{n}={145}^o$
${180}^{o}n-{145}^{o}n={360}^o$
$n=\frac{360}{35}$
$n=\frac{72}{7}$
Since, n (number of sides) is not an integer, therefore it is not possible to exist a polygon whose each interior angles is ${145}^o$