Chapter 2.4, Problem 8PSA

To determine

To Prove: $\angle 5\cong \angle 8$

Answer to Problem 8PSA

  $\angle 5\cong \angle 8$

Explanation of Solution

Given information: $\because \angle 6\cong \angle 7$

  

  $\because$ ROSE in a line. Then by linear pair

Axiom,

  $\begin{array}{l}\angle 5+\angle 6={180}^{\circ }and\angle 7+\angle 8={180}^{\circ }\\ \therefore \angle 5+\angle 6=\angle 7+\angle 8.\end{array}$

But given that

  $\begin{array}{l}\angle 5=\angle 6\\ \therefore \angle 5+\angle 7=\angle 7+\angle 8\\ \therefore \angle 5+\angle 8.\end{array}$