Question

If two angles are complementary of each other, then each angle is:
\[
  \left( a \right){\text{An obtuse angle}} \\
  \left( b \right){\text{A right angle}} \\
  \left( c \right){\text{An acute angle}} \\
  \left( d \right){\text{A supplementary angle}} \\
 \]

Answer 1

Hint-In this question, we use the concept of complementary angle and acute angle. Complementary angles are two angles whose sum is 900 and an acute angle is an angle that measures less than 900.

Complete step-by-step answer:
Given, two angles are complementary to each other that means the sum of two angles is 900.

We can see $\angle POQ{\text{ and }}\angle {\text{QOR}}$ are complementary angles and the sum of both the angles are ${90^0}$ .
$ \Rightarrow \angle POQ + \angle QOR = {90^0}$
Now, the sum of two angles is 900 so we can say both angles are less than 900.
\[ \Rightarrow \angle POQ,\angle QOR < {90^0}\]
If any angle that measures less than 900 so that is an acute angle.
Hence, $\angle POQ{\text{ and }}\angle {\text{QOR}}$ are acute angles.
So, the correct option is (c).

Note-In such types of problems we have to use a diagram of two complementary angles and observe if the sum of any two angles are 900 so individually both angles are less than 900. So, this statement is always true that If two angles are complementary to each other, then each angle is an acute angle.