Question

Find the measure of each interior angle of a regular polygon having
(i) 10 sides
(ii) 15 sides.

Answer 1

For a regular polygon with n sides:
$\mathrm{Each}\mathrm{interior}\mathrm{angle}=180-\left\{\mathrm{Each}\mathrm{exterior}\mathrm{angle}\right\}=180-\left(\frac{360}{\mathrm{n}}\right)$

(i) For a polygon with 10 sides:
$$\begin{gathered} \mathrm{Each}\mathrm{exterior}\mathrm{angle}=\frac{360}{10}={36}^{\mathrm{o}} \\ \Rightarrow \mathrm{Each}\mathrm{interior}\mathrm{angle}=180-36={144}^{\mathrm{o}} \end{gathered}$$

(ii) For a polygon with 15 sides:
$$\begin{gathered} \mathrm{Each}\mathrm{exterior}\mathrm{angle}=\frac{360}{15}={24}^{\mathrm{o}} \\ \Rightarrow \mathrm{Each}\mathrm{interior}\mathrm{angle}=180-24={156}^{\mathrm{o}} \end{gathered}$$