Find the angle which is four times its complement. - Vidyadip

Question

Find the angle which is four times its complement.

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Answer

Let the measure of the required angle be $x$.
Then, measure of its complement $= (90^\circ - x).$
Therefore, $x = (90^\circ - x)4$
$\Rightarrow x = 360^\circ - 4x$
$\Rightarrow 5x = 360^\circ $
$\Rightarrow x = 72^\circ $
Hence, the measure of the required angle is $72^\circ $.

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