Answer

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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 $90{}^\circ -x$.

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 $ .

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 $ .

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