Question

There is a regular polygon whose each interior angle is ${175}^{\circ }$

State true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Given, a polygon whose each interior angles is ${175}^o$
Sum of interior angles of a polygon is = ${180}^o(n-2)$
Each interior angle of a polygon = $\frac{{180}^o(n-2)}{n}$
$\frac{{180}^o(n-2)}{n}={175}^o$
${180}^{o}n-{175}^{o}n={360}^o$
$n=\frac{360}{5}$
$n=72$
Since, n (number of sides) is an integer, therefore there exist a polygon whose each interior angles is ${175}^o$