Question

Find the complement of each of the following angles.

Answer 1

Hint: To find a complement of any angle we subtract the given angle from ${{90}^{\circ }}$. We can also say if two angles are complementary then their sum will be ${{90}^{\circ }}$.

Complete step by step solution:
(a)

Given angle is ${{60}^{\circ }}$.
For finding a complement of a given angle we can subtract it from ${{90}^{\circ }}$.
So complement of given angle is ${{90}^{\circ }}-{{60}^{\circ }}={{30}^{\circ }}$
So we can say the complement angle of ${{60}^{\circ }}$angle is ${{30}^{\circ }}$.
(b)

  Given angle is ${{82}^{\circ }}$.
Complement angle of ${{82}^{\circ }}$ is ${{90}^{\circ }}-{{82}^{\circ }}={{8}^{\circ }}$

Hence the complement angle of ${{82}^{\circ }}$is ${{8}^{\circ }}$.

Note: If two angles are complement to each other then their sum should be ${{90}^{\circ }}$. So If we need to find complement angle of any given angle we should check given angle is less than ${{90}^{\circ }}$ or not because if given angle is greater than ${{90}^{\circ }}$then its complement angle is not possible.