Question

If the complement of an angle is one fourth of its supplement then find the angle.

Answer 1

Let $x$ be the angle.

The complement of the angle is ${90}^{\circ }-x$.

The supplement of the angle is ${180}^{\circ }-x$.

According to the question,

${90}^{\circ }-x=\frac{1}{4}\left({180}^{\circ }-x\right)$

$4\left({90}^{\circ }-x\right)={180}^{\circ }-x$

${360}^{\circ }-4x={180}^{\circ }-x$

${360}^{\circ }-{180}^{\circ }=3x$

${180}^{\circ }=3x$

$x={60}^{\circ }$