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

Exterior angle of an n-sided polygon = ${\left(\frac{360}{n}\right)}^o$
(i) For a pentagon: $$\begin{gathered} n=5 \\ \therefore \left(\frac{360}{n}\right)=\left(\frac{360}{5}\right)={72}^o \end{gathered}$$

(ii) For a hexagon: $$\begin{gathered} n=6 \\ \therefore \left(\frac{360}{n}\right)=\left(\frac{360}{6}\right)={60}^o \end{gathered}$$


(iii) For a heptagon: $$\begin{gathered} n=7 \\ \therefore \left(\frac{360}{n}\right)=\left(\frac{360}{7}\right)=51.{43}^o \end{gathered}$$


(iv) For a decagon: $$\begin{gathered} n=10 \\ \therefore \left(\frac{360}{n}\right)=\left(\frac{360}{10}\right)={36}^o \end{gathered}$$

(v) For a polygon of 15 sides: $$\begin{gathered} n=15 \\ \therefore \left(\frac{360}{n}\right)=\left(\frac{360}{15}\right)={24}^o \end{gathered}$$