Chapter 12, Problem 1MCQ

To determine

To state:whether the angles are complementary, supplementary or neither.

Answer to Problem 1MCQ

the angles are supplementary.

Explanation of Solution

Given : the angles provided in the question,

  $m\angle 1={54}^{\circ }$

  $m\angle 2={126}^{\circ }$

to find that the given angles are supplementary or complementary, find their sum if the sum is ${90}^{\circ }$ then they are complementary, if the sum of their angles is ${180}^{\circ }$ then they are supplementary.

  $m\angle 1={54}^{\circ }$

  $m\angle 2={126}^{\circ }$

  $\begin{array}{l}m\angle 2+m\angle 1={126}^{\circ }+{54}^{\circ }\text{ [substitute]}\\ m\angle 2+m\angle 1={180}^{\circ }\text{ [add]}\end{array}$

So the angles are supplementary.

Hence,the angles are supplementary.