Question

The measure of the complementary of the angle of measure $90{}^\circ $ is
[a] $0{}^\circ $
[b] $45{}^\circ $
[c] $90{}^\circ $
[d] $60{}^\circ $

Answer 1

Hint: The measure of complementary angles add up to $90{}^\circ $. So let x be the measure of complementary angles. Create a linear equation in x. Solve for x. The value of x gives the measure of the complementary angle. Alternatively, you can directly use the complementary angle of measure x is $90{}^\circ -x$.

Complete step-by-step answer:
Complementary angles: Two angles whose measures add up to $90{}^\circ $ are called complementary angles, e.g. $60{}^\circ $ and $30{}^\circ $ are complementary angles.
Supplementary angles: Two angles whose measures add up to $180{}^\circ $ are called supplementary angles, e.g. $60{}^\circ $ and $120{}^\circ $
Reflex angle of an angle: The measure of an angle and its reflex sum up to $360{}^\circ $.
Let the measure of complementary angle be x.
Since $90{}^\circ $ and x are complementary we have
$90{}^\circ +x=90{}^\circ $
Subtracting $90{}^\circ $ from both sides, we get
\[\begin{align}
  & 90{}^\circ +x-90{}^\circ =90{}^\circ -90 \\
 & \Rightarrow x=0{}^\circ \\
\end{align}\]
Hence the measure of the complementary angle of $90{}^\circ $ is $0{}^\circ $.
Hence option [a] is correct.

Note: [1] There is usually a confusion whether supplementary angles sum up to $180{}^\circ $ or whether complementary angles add up to $180{}^\circ $. In that case, one can memorise as follows:
In the English alphabet, s comes after c. So s>c. So, supplementary angles add up to $180{}^\circ $ , and complementary angles add up to $90{}^\circ $ .