Question
An angle is equal to $8$ times its complement. Determine its measure.
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Answer
Let the measure of an angle be $x^\circ .$
Therefore, its complement will be $(90 - x)^\circ .$
It is given that
$\Rightarrow x^\circ = 8(90 - x)^\circ $
$\Rightarrow x = 720 - 8x$
$\Rightarrow 9x = 720$
$\Rightarrow x = 80$
Therefore, the measure of the angles is $80^\circ $
Therefore, its complement will be $(90 - x)^\circ .$
It is given that
$\Rightarrow x^\circ = 8(90 - x)^\circ $
$\Rightarrow x = 720 - 8x$
$\Rightarrow 9x = 720$
$\Rightarrow x = 80$
Therefore, the measure of the angles is $80^\circ $
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