Question

How do you find the complement and supplement of \[{{150}^{\circ }}\]?

Answer 1

Hint: In this problem, we have to find the supplement and the compliment for the given degree. We know that two angles are said to be complementary angles, if their sum is one right angle i.e. \[{{90}^{\circ }}\]and two angles are said to be supplementary angles, if their sum is two right angles i.e. \[{{180}^{\circ }}\] . So, we can add the given number to which it gives \[{{180}^{\circ }}\] for supplement and can subtract the number for which it gives \[{{90}^{\circ }}\]to find the complement.

Complete step by step solution:
We know that the angle given is \[{{150}^{\circ }}\].
We also know that,
Two angles are said to be complementary angles, if their sum is one right angle i.e. \[{{90}^{\circ }}\].
Two angles are said to be supplementary angles, if their sum is two right angles i.e. \[{{180}^{\circ }}\].
To find the supplement, we can add the given angle to some unknown variable ‘x’ which is equal to \[{{180}^{\circ }}\] .
\[\begin{align}
  & \Rightarrow {{150}^{\circ }}+x={{180}^{\circ }} \\
 & \Rightarrow x={{180}^{\circ }}-{{150}^{\circ }} \\
 & \Rightarrow x={{30}^{\circ }} \\
\end{align}\]
Therefore, the supplement of \[{{150}^{\circ }}\] is \[{{30}^{\circ }}\].
 To find the complement, we can add the given angle to some unknown variable ‘y’ which is equal to \[{{90}^{\circ }}\].
\[\begin{align}
  & \Rightarrow {{150}^{\circ }}+y={{90}^{\circ }} \\
 & \Rightarrow y={{90}^{\circ }}-{{150}^{\circ }} \\
 & \Rightarrow y=-{{60}^{\circ }} \\
\end{align}\]
Therefore, the complement of \[{{150}^{\circ }}\]is \[-{{60}^{\circ }}\].

Note: Students should understand the concept of complementary angles and the supplementary angles. We should always remember that, we can add the given number to which it gives \[{{180}^{\circ }}\] for supplement and can subtract the number for which it gives \[{{90}^{\circ }}\]to find the complement.