Question

Find the measure of each exterior angle of a regular (i) pentagon (ii) hexagon (iii) heptagon (iv) decagon (v) polygon of 15 sides.

Answer 1

We know that sum of exterior angles of a polygon is ${360}^{\circ }$ Then, (i) Pentagon's exterior angle = $\frac{{360}^{\circ }}{5}={72}^{\circ }$ (ii)Hexagon's exterior angle = $\frac{{360}^{\circ }}{6}={60}^{\circ }$ (iii) Heptagon's exterior angle = $\frac{{360}^{\circ }}{7}=51\frac{3^{\circ }}{7}=\left({51.4}^{\circ }\right)$ (iv) Decagon's exterior angle = $\frac{{360}^{\circ }}{10}={36}^{\circ }$ (v) and exterior angle of a polygon of 15 sides = $\frac{{360}^{\circ }}{15}={24}^{\circ }$