Question

Find the angle whose complement is one-third of its supplement.

Answer 1

Let the measure of the required angle be $x°$.
Then, the measure of its complement $=\left(90-x\right)°$.
And the measure of its supplement$=\left(180-x\right)°$.
Therefore,
$$\begin{gathered} \left(90-x\right)=\frac{1}{3}\left(180-x\right) \\ \Rightarrow 3\left(90-x\right)=\left(180-x\right) \\ \Rightarrow 270-3x=180-x \\ \Rightarrow 2x=90 \\ \Rightarrow x=45 \end{gathered}$$
Hence, the measure of the required angle is $45°$.