Chapter 12.1, Problem 22E

To determine

To Calculate: The other angle of a supplementary angle pair when one angle is given.

Answer to Problem 22E

The measure of the angle that is supplementary to an angle measuring ${137}^o$ is ${43}^o$ .

Explanation of Solution

Given Information: Two angles are a supplementary angle pair and one of the angles measures ${160}^o$ .

Concept Used: If the sum of measures two angles is ${90}^o$ then the angles are called complementary angles and if the sum is ${180}^o$ then the angles are called supplementary angles.

Calculation: Since $\angle 1$ and $\angle 2$ are supplementary angles

  $m\angle 1+m\angle 2={180}^o$

  $\Rightarrow {137}^o+m\angle 2={180}^o$

  $\Rightarrow m\angle 2={180}^o-{137}^o={43}^o$$$

Therefore, the measure of the supplementary angle of an angle measuring ${137}^o$ is $43^o$ .