Question

State true or false:

Is it possible to have a regular polygon whose each interior angle is ${175}^{\circ }$

• A. True
• B. False

Answer 1

The correct option is A True

Each interior angle of regular polygon of $n$ sides is given by $\frac{{180}^o(n-2)}{n}$
According to question

$\frac{{180}^o(n-2)}{n}={175}^0$
$\Rightarrow {180}^o(n-2)=175n$
$\Rightarrow 180n-{360}^o=175n$
$\Rightarrow 5n={360}^o$
$\Rightarrow n=72$

Clearly there is a polygon of sides $72$ whose each interior angle is ${175}^0$