Find the angle whose supplement is four times its complement. - Vidyadip

Question

Find the angle whose supplement is four times its complement.

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Answer

Let the measure of the required angle be $x^\circ $.
Then, measure of its complement $= (90 - x)^\circ $.
And, measure of its supplement $= (180 - x)^\circ . (180 - x) = 4 (90 - x) $
$\Rightarrow 180 - x = 360 - 4x$
$ \Rightarrow 3x = 180 $
$\Rightarrow x = 60$
Hence, the measure of the required angle is 60º.

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