Chapter 2.4, Problem 6PSA

To determine

To Draw: Conclusions from given information.

Answer to Problem 6PSA

  $\angle 6\cong \angle 7$ , $\angle 4$ is supplementary to $\angle 7$ , $\angle 5$ is supplementary to $\angle 6$ .

Explanation of Solution

Given information:

  $\angle 4$ Is supplementary to $\angle 6$ , $\angle 5$ is supplementary to $\angle 7$ . $\angle 4\cong \angle 5$

given that $\angle 4$ is supplementary to $\angle 7$ , $\angle 5$ is supplementary to $\angle 6$ .

  $\begin{array}{l}\because \angle 4+\angle 7={180}^{\circ },\angle 6+\angle 5={180}^{\circ }\\ \therefore \angle 4+\angle 7=\angle 6+\angle 5\\ \therefore \angle 4+\angle 6=\angle 6+\angle \mathrm{5....}(given\angle 6=\angle 7)\\ \therefore \angle 4=\angle 5\\ Also,\angle 5+\angle 7={180}^{\circ }and\angle 6+\angle 4={180}^{\circ }\end{array}$