Question
Find the angle whose complement is one-third of its supplement.
✓
Answer
Let the measure of the required angle be $x^\circ $.
Then, the measure of its complement $= (90 - x)^\circ $.
And the measure of its supplement $= (180 - x)^\circ $.
Therefore, $(90 - \text{x}) = \frac{1}{3}(180-\text{x})$
$\Rightarrow 3(90 - x) = (180 - x)$
$ \Rightarrow 270 - 3x = 180 - x $
$\Rightarrow 2x = 90 $
$\Rightarrow x = 45$
Hence, the measure of the required angle is $45^\circ $.
Then, the measure of its complement $= (90 - x)^\circ $.
And the measure of its supplement $= (180 - x)^\circ $.
Therefore, $(90 - \text{x}) = \frac{1}{3}(180-\text{x})$
$\Rightarrow 3(90 - x) = (180 - x)$
$ \Rightarrow 270 - 3x = 180 - x $
$\Rightarrow 2x = 90 $
$\Rightarrow x = 45$
Hence, the measure of the required angle is $45^\circ $.
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