Question

The exterior and interior angle of a regular polygon are in the ratio 1:9. Find. i)number of sides of polygon ii)Sum of interior angles of polygon

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \mathrm{Exterior}\mathrm{angle}=\frac{360}{\mathrm{n}} \\ \mathrm{and}\mathrm{interior}\mathrm{angle}=180-\frac{360}{\mathrm{n}} \\ \mathrm{So}\mathrm{here} \\ \frac{\frac{360}{\mathrm{n}}}{180-\frac{360}{\mathrm{n}}}=\frac{1}{9} \\ \frac{360}{180\mathrm{n}-360}=\frac{1}{9} \\ \frac{2}{\mathrm{n}-2}=\frac{1}{9} \\ \mathrm{n}-2=18 \\ \mathrm{n}=20 \\ \mathrm{So}\mathrm{number}\mathrm{of}\mathrm{side}=20 \\ \mathrm{and}\mathrm{sum}\mathrm{of}\mathrm{interior}\mathrm{angle}=\mathrm{n}\times \left(180-\frac{360}{\mathrm{n}}\right) \\ =20\left(180-\frac{360}{20}\right)=3240\mathrm{degree} \\ \mathrm{Regards} \end{gathered}$$