Question

1 fill in the blank 2 points
\\( \overrightarrow{qs}\\) is the angle bisector of \\(\angle pqr\\). \\(m\angle sqr = 22^{circ}\\). what is \\(m\angle pqs\\)? what is \\(m\angle pqr\\)?
\\(m\angle pqs=) type your answer...
\\(m\angle pqr=) type your answer...

Explanation:

Step1: Recall angle - bisector property

An angle bisector divides an angle into two equal angles. Since $\overrightarrow{QS}$ is the angle - bisector of $\angle PQR$, then $\angle PQS=\angle SQR$.

Step2: Find $m\angle PQS$

Given $m\angle SQR = 22^{\circ}$, so $m\angle PQS=22^{\circ}$ (because $\angle PQS=\angle SQR$).

Step3: Find $m\angle PQR$

Since $\angle PQR=\angle PQS+\angle SQR$ and $\angle PQS = \angle SQR=22^{\circ}$, then $m\angle PQR=22^{\circ}+22^{\circ}=44^{\circ}$.

Answer:

$m\angle PQS = 22^{\circ}$
$m\angle PQR = 44^{\circ}$