Question

angle which is one fifth of its supplement

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{measure}\mathrm{of}\mathrm{required}\mathrm{angle}=\mathrm{x} \\ \mathrm{Now},\mathrm{measure}\mathrm{of}\mathrm{its}\mathrm{supplement}=180°-\mathrm{x} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}, \\ \mathrm{x}=\frac{1}{5}\left(180°-\mathrm{x}\right) \\ \Rightarrow 5\mathrm{x}=180°-\mathrm{x} \\ \Rightarrow 5\mathrm{x}+\mathrm{x}=180° \\ \Rightarrow 6\mathrm{x}=180° \\ \Rightarrow \mathrm{x}=30° \\ \mathrm{So},\mathrm{the}\mathrm{required}\mathrm{angle}=30° \end{gathered}$$