Question

Is it possible to have a regular polygon whose each interior angle is ${138}^{\circ }$

State true or false:

• A. True
• B. False

Answer 1

The correct option is B False

Let number of polygon = n (which must be an integer)
Sum of all interior angles is $n\times {138}^o$
Sum of all interior angles of a polygon is ${180}^o(n-2)$
$=>n\times {138}^o={180}^o(n-2)$
$=>{42}^{o}n={360}^o$
$=>n=\frac{60}{7}$
Their is no possibility to have a regular polygon whose each interior angle is ${138}^o$