Question

If x° is the measure of an angle which is equal to its complement and y° is the measure of an angle which is equal to its supplement, then $\frac{x°}{y°}$ is equal to ___________.

Answer 1

Two angles are complementary if their sum is 90º.
$$\begin{gathered} \therefore x°=90°-x° \\ \Rightarrow 2x°=90° \\ \Rightarrow x°=45° \end{gathered}$$

Two angles are supplementary if their sum is 180º.
$$\begin{gathered} \therefore y°=180°-y° \\ \Rightarrow 2y°=180° \\ \Rightarrow y°=90° \end{gathered}$$

$\therefore \frac{x°}{y°}=\frac{45°}{90°}=\frac{1}{2}$

If x° is the measure of an angle which is equal to its complement and y° is the measure of an angle which is equal to its supplement, then $\frac{x°}{y°}$ is equal to $\underline{\frac{1}{2}}$.