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The supplement of an angle is one third of the given angle. Find the measures of the given angle and its supplement.

Solution

Let the measure of the given angle be $x^{\circ}$.

Then, the measure of its supplement $=(180-x)^{\circ}$.

$\therefore 180-x=\frac{1}{3} x \Rightarrow 3(180-x)=x$

$\Rightarrow 540-3 x=x$

$\Rightarrow 4 x=540 \Rightarrow x=135$.

Hence, the measure of the given angle is $135^{\circ}$ and the measure of its supplement is $(180-135)^{\circ}=45^{\circ}$.

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