Question

qs is the angle bisector of ∠pqr. find m∠sqr and m∠pqr. (5 pts)

m∠sqr =
degrees

m∠pqr =
degrees

Explanation:

Step1: Recall angle - bisector property

An angle bisector divides an angle into two equal parts. Given that $\angle PQS = 80^{\circ}$ and $\overrightarrow{QS}$ is the angle - bisector of $\angle PQR$, then $\angle SQR=\angle PQS$.

Step2: Find $m\angle SQR$

Since $\angle SQR=\angle PQS$ and $\angle PQS = 80^{\circ}$, so $m\angle SQR = 80^{\circ}$.

Step3: Find $m\angle PQR$

Since $\overrightarrow{QS}$ bisects $\angle PQR$, then $m\angle PQR=2\times m\angle SQR$. Substituting $m\angle SQR = 80^{\circ}$, we get $m\angle PQR = 160^{\circ}$.

Answer:

$m\angle SQR = 80$ degrees
$m\angle PQR = 160$ degrees