Question

qs bisects ∠pqr. use the diagram and the given angle measure to find the indicated angle measures. (see example 5.) 34) ( mangle rqs = 71^circ ). find ( mangle pqs ) and ( mangle pqr ).

Explanation:

Step1: Define angle bisector property

A bisector splits an angle into two equal angles, so $m\angle RQS = m\angle PQS$.

Step2: Find $m\angle PQS$

Given $m\angle RQS = 71^\circ$, substitute into the equality:
$m\angle PQS = 71^\circ$

Step3: Calculate $m\angle PQR$

$\angle PQR$ is the sum of $\angle RQS$ and $\angle PQS$:
$m\angle PQR = m\angle RQS + m\angle PQS = 71^\circ + 71^\circ$

Answer:

$m\angle PQS = 71^\circ$, $m\angle PQR = 142^\circ$