Question

If an angle is half of its complementary angle then find its measure

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{required}\mathrm{angle}=\mathrm{x} \\ \mathrm{Measure}\mathrm{of}\mathrm{its}\mathrm{complement}=90°-\mathrm{x} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ \mathrm{x}=\frac{1}{2}\left(90°-\mathrm{x}\right) \\ \Rightarrow 2\mathrm{x}=90°-\mathrm{x} \\ \Rightarrow 3\mathrm{x}=90° \\ \Rightarrow \mathrm{x}=30° \\ \mathrm{So},\mathrm{required}\mathrm{angle}=30° \end{gathered}$$