Question

Find the measure of each exterior angle of a regular polygon of 9 sides.

Answer 1

(i) Sum of angles of a regular polygon $=(n-2)\times {180}^{\circ }$
$=(9-2)\times {180}^{\circ }=7\times {180}^{\circ }={1260}^{\circ }$
Each interior angle $=\frac{Sumofinteriorangles}{Numberofsides}=\frac{{1260}^{\circ }}{9}={140}^{\circ }$
Each exterior angle $={180}^{\circ }-{140}^{\circ }={40}^{\circ }$