Question

Find the measure of the supplementary angle pair of $ 138{}^\circ $ . (in degrees)

Answer 1

Hint: Supplementary angles means those angles where the sum of the angles is equal to $ 180{}^\circ $ . We have to find the pair of angles, which includes an angle of $ 138{}^\circ $ and whose sum is $ 180{}^\circ $ . WE can do so by assuming the unknown pair as X and forming an equation with the known angle so that their sum is equal to $ 180{}^\circ $ .

Complete step-by-step answer:
It is given in the question that we have to find the measure of the supplementary angle pair of $ 138{}^\circ $ . As we know, supplementary angles are basically a pair of angles, where the sum of the pair of the angles is equal to $ 180{}^\circ $ or we can say $ x+y=180{}^\circ $ . Now, to solve this question , let us assume the unknown angle as X. The other angle is known to us, that is, $ 138{}^\circ $ . So, it means that the sum of X and $ 138{}^\circ $ should be equal to $ 180{}^\circ $ .

So, we can write it as follows,
 $ X+138{}^\circ =180{}^\circ $
Now, we will transpose $ 138{}^\circ $ from the left hand side or the LHS to the right hand side or the RHS, So, we will get,
 $ \begin{align}
  & X=180{}^\circ -138{}^\circ \\
 & \Rightarrow X=42{}^\circ \\
\end{align} $
Therefore, the angle X is equal to $ 42{}^\circ $ and the supplementary pair of angles is $ \left( 138{}^\circ ,42{}^\circ \right) $ .

Note: There is a possibility that the students get confused with complementary and supplementary angles. If they are not clear of this basic concept, then they might get the incorrect answer. We can apply a simple trick to easily remember the meaning of complementary and supplementary angles, which is as follows : We know that alphabet C comes before S and that $ 90{}^\circ $ comes before $ 180{}^\circ $ , so we can memorise it as follows, $ C-90{}^\circ $ and $ S-180{}^\circ $ or as $ C