Mathematics

Finf the angle, if its supplement is three times of its complement.


ANSWER

45


SOLUTION
Let the required angle be $$x.$$ 
Its complement $$=\left( 90-x \right)$$ & its supplement $$=\left( 180-x \right)$$ 
Given that, Its supplement $$=3$$ times of its complement,
$$ \Rightarrow \left( 180-x \right) =3\times \left( 90-x \right) $$ 
$$\Rightarrow 180-x=270-3x$$ 
$$\Rightarrow 3x-x=270-180$$ 
$$\Rightarrow 2x=90$$ 
$$\Rightarrow x={ 45 }^{ o }$$
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