Question

Find the angle, if its complement is one-fourth of its supplement.

Answer 1

Let the required angle be $x.$

Its complement $=(90-x)$ & its supplement $=(180-x)$.

Given that, Its complement $=\frac{1}{4}$ of its supplement.

$\Rightarrow (90-x)=\frac{1}{4}\times (180-x)$

$\Rightarrow 360-4x=180-x$

$\Rightarrow 4x-x=360-180$

$\Rightarrow 3x=180$

$\Rightarrow x=\frac{180}{3}$

$\Rightarrow x={60}^o$