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

Last updated date: 27th Mar 2023
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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 $90{}^\circ -x$.

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 $360{}^\circ$.
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 $0{}^\circ$.
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 $90{}^\circ$ .