Question

analyzing angle bisectors $overrightarrow{qs}$ is the angle bisector of $angle pqr$. find the two angle measures not given in the diagram. 38.

Explanation:

Step1: Recall angle - bisector property

An angle bisector divides an angle into two equal angles. Let $\angle PQS=\angle SQR = x$.

Step2: Set up an equation

We know that $\angle PQR=\angle PQS+\angle SQR$ and $\angle PQR = 91^{\circ}$. So $x + x=91^{\circ}$, or $2x = 91^{\circ}$.

Step3: Solve for $x$

Dividing both sides of the equation $2x = 91^{\circ}$ by 2, we get $x=\frac{91^{\circ}}{2}=45.5^{\circ}$. So $\angle PQS = 45.5^{\circ}$ and $\angle SQR=45.5^{\circ}$.

Answer:

$\angle PQS = 45.5^{\circ}$, $\angle SQR = 45.5^{\circ}$