Question

If the supplement of an angle is three times its complement, find the angle.

Answer 1

Let the required angle = x
Then its complement angle = ${90}^{\circ }-x$
and supplement angle = ${180}^{\circ }-x$
$\therefore {180}^{\circ }-x=3({90}^{\circ }-x)\Rightarrow {180}^{\circ }-x={270}^{\circ }-3x\Rightarrow -x+3x={270}^{\circ }-{180}^{\circ }\Rightarrow 2x={90}^{\circ }\Rightarrow x=\frac{{90}^{\circ }}{2}={45}^{\circ }$
$\therefore$ Required angle = ${45}^{\circ }$