Mathematics

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

60

SOLUTION
Let the required angle be $x.$
Its complement $=\left( 90-x \right)$ & its supplement $=\left( 180-x \right)$.
Given that, Its complement $=\cfrac { 1 }{ 4 }$ of its supplement.
$\Rightarrow \left( 90-x \right) =\cfrac { 1 }{ 4 } \times \left( 180-x \right)$
$\Rightarrow 360-4x=180-x$
$\Rightarrow 4x-x=360-180$
$\Rightarrow 3x=180$
$\Rightarrow x=\cfrac { 180 }{ 3 }$
$\Rightarrow x={ 60 }^{ o }$

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