Question

The interior angle of a convex regular polygon is four times the exterior angle. Find the number of sides.

Answer 1

$\begin{array}{c}\Rightarrow 4timestheenteriorangle+exteriorangleis{180}^{\circ }\\ \Rightarrow 5xexteriorangle={180}^{\circ }\\ \Rightarrow exteriorangle={36}^{\circ }\\ Then,numberofsidesofpolygon=\frac{{360}^{\circ }}{{36}^{\circ }}=10Ans.\end{array}$