Mathematics

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


ANSWER

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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