Question

The sum of the measure of the supplementary angle is _____.

Answer 1

Hint: Understand the meaning of the term supplementary angles by considering examples of a linear pair of angles A and B. Determine the sum of these angles formed on a straight line to get the answer.

Complete step-by-step solution
Here, we have been given an incomplete statement, “the sum of the measure of a supplementary angle is ______”, and we have to complete it by filling the empty space. So, first, let us learn about supplementary angles.
The term supplementary angles are used for two angles. Two angles are called supplementary angles when their sum is equal to 180 degrees. For example: - \[{{30}^{\circ }}\] and \[{{150}^{\circ }}\], \[{{90}^{\circ }}\] and \[{{90}^{\circ }}\], \[{{60}^{\circ }}\] and \[{{120}^{\circ }}\] are some pairs of supplementary angles. When two angles are supplementary then they are called supplements of each other. For example: - \[{{30}^{\circ }}\] and \[{{150}^{\circ }}\] are a supplement of each other.
Now, let us consider a linear pair of angles.

A linear pair of angles are formed when the angle of a straight line is divided into two parts by any line. In the above figure, we have considered a straight line AOB whose angle is divided into two parts by the line OM. We have assumed \[\angle AOM=\angle A\] and \[\angle BOM=\angle B\]. We know that the total angle formed at the center of a straight line is \[{{180}^{\circ }}\]. So, we have,
\[\begin{align}
  & \Rightarrow \angle AOB={{180}^{\circ }} \\
 & \Rightarrow \angle AOM+\angle BOM={{180}^{\circ }} \\
 & \Rightarrow \angle A+\angle B={{180}^{\circ }} \\
\end{align}\]
Hence, we can conclude that a linear pair of angles are always supplementary.
Therefore, the given statement can be completed as: -
“The sum of the measure of supplementary angles is \[{{180}^{\circ }}\]”.

Note: One may note that even if the sum of three or more angles is \[{{180}^{\circ }}\], they cannot be called supplementary angles because this term is used for a pair of angles only. Note that there is another term called complementary angles. These are a pair of angles whose sum is \[{{90}^{\circ }}\]. So, remember the definitions of the two terms so that you may not get confused.