Question

fill in the blank 2 points
$overleftrightarrow{qs}$ is the angle bisector of $angle pqr$. $mangle sqr = 22^circ$. what is $mangle pqs$? what is $mangle pqr$?
diagram: point q with rays to p, s, r (p above s, s above r)
$mangle pqs =$ type your answer... $^circ$
$mangle pqr =$ type your answer... $^circ$

Explanation:

Step1: Recall angle bisector definition

An angle bisector divides an angle into two equal - measure angles. Since \(\overrightarrow{QS}\) is the angle bisector of \(\angle PQR\), we know that \(m\angle PQS=m\angle SQR\).
Given that \(m\angle SQR = 22^{\circ}\), so \(m\angle PQS=22^{\circ}\).

Step2: Calculate \(m\angle PQR\)

We know that \(\angle PQR=\angle PQS+\angle SQR\). Since \(m\angle PQS = m\angle SQR=22^{\circ}\), then \(m\angle PQR=22^{\circ}+22^{\circ}=44^{\circ}\).

Answer:

\(m\angle PQS = 22^{\circ}\), \(m\angle PQR = 44^{\circ}\)