Chapter 12.1, Problem 46E

To determine

To prove: The other angle $m\angle 4$ .

Answer to Problem 46E

The measure of the angle $m\angle 4={108}^{\circ }$ .

Explanation of Solution

Given: Angle

  $m\angle 3={72}^{\circ }$ .

Calculation:

Since, sum of the angles forming a linear pair is ${180}^{\circ }$ .

Therefore,

  $m\angle 3+m\angle 4={180}^{\circ }$..........(1)

Find $m\angle 4$ using equation (1)

  $m\angle 3+m\angle 4={180}^{\circ }$

  $\begin{array}{l}\Rightarrow {72}^{\circ }+m\angle 4={180}^{\circ }\\ \Rightarrow m\angle 4={180}^{\circ }-m\angle 3\\ \Rightarrow m\angle 4={180}^{\circ }-{72}^{\circ }\\ \Rightarrow m\angle 4={108}^{\circ }\end{array}$

Therefore,

  $m\angle 4={108}^{\circ }$

Conclusion:

Thus, option H

  $={108}^{\circ }$ is the correct choice.