Question

Find the number of sides of a regular polygon, when each of its angles has a measure of ${175}^o$

• A. $60$
• B. $52$
• C. $72$
• D. $98$

Answer 1

The correct option is C $72$

Each interior angle of a regular polygon = $\frac{{180}^o(n-2)}{n}$ where n = number of sides of polygon.
Given, each of its angles has a measure of ${175}^o$.
$\frac{{180}^o(n-2)}{n}={175}^o$
$=>{180}^{o}n-{175}^{o}n={360}^o$
$=>5^{o}n={360}^o$
$=>n=72$