Question

Is it possible to have a regular polygon if each interior angle is ${105}^{\circ }$

Answer 1

Exterior angle$+$interior angle$={180}^0$

Exterior angle$={75}^0$

Number of sides$=\frac{{360}^0}{exteriorangle}$

$=\frac{{360}^0}{{75}^0}$

As number of slides is not an integer so it is not possible to have a regular polygon whose each interior angle is ${105}^0$