Chapter 2.6, Problem 12PSB

To determine

To Verify: $\angle 2=\angle 3.$

Explanation of Solution

Given information: PR bisects $\angle QPS$ , KO bisects $\angle JKM$ .

  $\angle 1$ Is supplementary to $\angle JKM$ , $\angle 1$ is supplementary to $\angle QPS$ .

Verification:

  $\angle 1+\angle JKM={180}^{\circ }$ and $\angle 1+\angle QPS={180}^{\circ }$

  $\therefore \angle JKM=\angle QPS\mathrm{....}(1)$

Now PR and KO are angle bisects, then from equation (1)

  $\begin{array}{l}2\angle 3=2\angle 2\\ \therefore \angle 3=\angle 2\end{array}$