Angles Bisecting: Solving for Angle Measures

When a line bisects an angle, it divides the angle into two equal parts. In this scenario, line Q bisects angle PQR, which means that it splits it into two equal angles. Given that the measure of angle RQS is 71°, we can determine the measures of angles PQS and PQR.

Since angle PQS is one of the bisected angles by line Q, and it bisects angle PQR evenly, the measure of angle PQS is also 71°. This is because the line evenly divides the angle, resulting in two equal parts.

To find the measure of angle PQR, we need to add the measures of the two bisected angles (PQS and RQS). Adding 71° (PQS) and 71° (RQS) results in a total of 142° for the entire angle PQR.

Therefore, the answer to the question is that the measure of angle PQS is 71°, and the measure of angle PQR is 142°. The line Q evenly bisects angle PQR, resulting in the angle measures provided.