Question

If the complement of an angle is equal to the supplement of the thrice of it. Find the measure of the angle.

Answer 1

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