Question

Find the number of sides of a regular polygon whose each exterior angle measures:
(i) 40°
(ii) 36°
(iii) 72°
(iv) 30°

Answer 1

Sum of all the exterior angles of a regular polygon is ${360}^o$​.

(i)
$$\begin{gathered} \mathrm{Each}\mathrm{exterior}\mathrm{angle}={40}^o \\ \mathrm{Number}\mathrm{of}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{regular}\mathrm{polygon}=\frac{360}{40}=9 \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{Each}\mathrm{exterior}\mathrm{angle}={36}^o \\ \mathrm{Number}\mathrm{of}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{regular}\mathrm{polygon}=\frac{360}{36}=10 \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{Each}\mathrm{exterior}\mathrm{angle}={72}^o \\ \mathrm{Number}\mathrm{of}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{regular}\mathrm{polygon}=\frac{360}{72}=5 \end{gathered}$$

(iv)
$$\begin{gathered} \mathrm{Each}\mathrm{exterior}\mathrm{angle}={30}^o \\ \mathrm{Number}\mathrm{of}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{regular}\mathrm{polygon}=\frac{360}{30}=12 \end{gathered}$$