What is the difference between supplementary angles and a linear pair?

Hint: From the given question we are asked to find out the difference between supplementary angles and a linear pair. For solving this question, we will take the help of the definitions of the supplementary angles and a linear pair and explain them briefly. After explaining them briefly, we will find the difference between them and solve the question.

Complete step-by-step solution:
In mathematics, we can use the sum of the measure of angles to categorize angles as different types. That is, if the sum of a pair of angles is equal to certain values, then they fall into the types defined by the sum.
Supplementary angles are defined with respect to the addition of two angles.
If the sum of two angles is said to be \[{{180}^{\circ }}\] then they are said to be supplementary angles, which forms a linear angle together.
For example,

Form the figure, we can say that
\[\begin{align}
  & \angle 1+\angle 2={{180}^{\circ }} \\
 & \Rightarrow {{100}^{\circ }}+{{80}^{\circ }}={{180}^{\circ }} \\
 & \therefore {{180}^{\circ }}={{180}^{\circ }} \\
\end{align}\]
Linear pair is a pair of adjacent angles whose noncommon sides form a straight line.

Linear pairs are also said to be pairs of two supplementary angles. But two supplementary angles can or cannot form a linear pair, they have to supplement each other, that is their sum is to be \[{{180}^{\circ }}\].
For example, if there are four linear pairs formed by two intersecting lines. Each pair forms supplementary angles because their sum is \[{{180}^{\circ }}\]. Or they might be two angles, their sum is \[{{180}^{\circ }}\], but they do not form a linear pair. Example is two angles in a parallelogram which share a common side.

Note: Students should have good knowledge in the concept of angles and it types. We must know the difference between supplementary angles and a linear pair to solve and find the difference between those angles.