Question

fill in the blank 2 points
$overrightarrow{qs}$ is the angle bisector of $angle pqr$, $mangle pqr = 91^circ$. what is $mangle pqs$? what is $mangle sqr?$
$mangle pqs = \text{type your answer...}^circ$
$mangle sqr = \text{type your answer...}^circ$

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, \( \overrightarrow{QS} \) bisecting \( \angle PQR \) means \( m\angle PQS = m\angle SQR \), and both are half of \( m\angle PQR \).

Step2: Calculate \( m\angle PQS \) and \( m\angle SQR \)

Given \( m\angle PQR = 91^\circ \), we find each angle by dividing by 2:
\( m\angle PQS = \frac{91^\circ}{2} = 45.5^\circ \)
\( m\angle SQR = \frac{91^\circ}{2} = 45.5^\circ \)

Answer:

\( m\angle PQS = \boldsymbol{45.5}^\circ \)
\( m\angle SQR = \boldsymbol{45.5}^\circ \)