Question

1. qs is the angle bisector of ∠pqr. find the two angle measures not given in the diagram.

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal angles.

Step2: Identify the known angle

We know that $\angle PQS = 40^{\circ}$.

Step3: Find the other angle

Since $\overline{QS}$ is the angle - bisector of $\angle PQR$, then $\angle SQR=\angle PQS = 40^{\circ}$, and $\angle PQR=\angle PQS+\angle SQR=40^{\circ}+40^{\circ} = 80^{\circ}$.

Answer:

$\angle SQR = 40^{\circ}$, $\angle PQR=80^{\circ}$