Question

Find the measure of an angle which is
(i) equal to its complement
(ii) equal to its supplement

Answer 1

(i) Let the measure of the required angle be $x°$.
Then, in case of complementary angles:
$$\begin{gathered} x+x=90° \\ \Rightarrow 2x=90° \\ \Rightarrow x=45° \end{gathered}$$
Hence, measure of the angle that is equal to its complement is $45°$.

(ii) Let the measure of the required angle be $x°$​.
Then, in case of supplementary angles:
$$\begin{gathered} x+x=180° \\ \Rightarrow 2x=180° \\ \Rightarrow x=90° \end{gathered}$$
Hence, measure of the angle that is equal to its supplement is $90°$.