Question

analyzing angle bisectors $overrightarrow{qs}$ is the angle bisector of $angle pqr$. 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: Calculate the measure of ∠PQS

Since $\overrightarrow{QS}$ is the angle - bisector of $\angle PQR$ and $\angle PQR = 124^{\circ}$, then $\angle PQS=\frac{1}{2}\angle PQR$. So, $\angle PQS=\frac{1}{2}\times124^{\circ}=62^{\circ}$.

Step3: Calculate the measure of ∠SQR

Since $\overrightarrow{QS}$ is the angle - bisector of $\angle PQR$, $\angle SQR=\angle PQS$. So, $\angle SQR = 62^{\circ}$.

Answer:

$\angle PQS = 62^{\circ}$, $\angle SQR = 62^{\circ}$