Chapter 12, Problem 16CP

To determine

To find: The measure of the supplement of $\angle 4$

Answer to Problem 16CP

The measure of the supplement of $\angle 4$ is ${172}^{\circ }$

Explanation of Solution

Given information : $\angle 3$ and $\angle 4$ are complementary angles and $m\angle 3={82}^{\circ }$

Concept used : If the sum of two angles are right angle or ${90}^{\circ }$ , then the angles are known as complementary angles. And the sum of two angles are ${180}^{\circ }$ , then the angles are known as supplementary angles.

Calculation :

$\angle 3$ and $\angle 4$ are complementary angles and $m\angle 3={82}^{\circ }$

So,

  $\begin{array}{l}m\angle 3+m\angle 4={90}^{\circ }\\ \Rightarrow {82}^{\circ }+m\angle 4={90}^{\circ }\\ \Rightarrow m\angle 4={90}^{\circ }-{82}^{\circ }\\ \Rightarrow m\angle 4=8^{\circ }\end{array}$

Supplement of $\angle 4$ is

  $\begin{array}{l}m\angle 4={180}^{\circ }-8^{\circ }\\ \Rightarrow m\angle 4={172}^{\circ }\end{array}$

Thus, the measure of the supplement of $\angle 4$ is ${172}^{\circ }$