Question

the measure of an angle is 6 times its component is 12 degree less than twice in supplement is

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{measure}\mathrm{of}\mathrm{an}\mathrm{angle}\mathrm{is}\mathrm{x}°. \\ \mathrm{Measure}\mathrm{of}\mathrm{its}\mathrm{complement}=\left(90°-\mathrm{x}\right) \\ \mathrm{measure}\mathrm{of}\mathrm{its}\mathrm{supplement}=\left(180°-\mathrm{x}\right) \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ 6\left(90°-\mathrm{x}\right)=2\left(180°-\mathrm{x}\right)-12° \\ \Rightarrow 540°-6\mathrm{x}=360°-2\mathrm{x}-12° \\ \Rightarrow 540°-6\mathrm{x}=348°-2\mathrm{x} \\ \Rightarrow 4\mathrm{x}=192° \\ \Rightarrow \mathrm{x}=48° \\ \mathrm{So},\mathrm{required}\mathrm{angle}\mathrm{is}48° \end{gathered}$$