ANSWER
m∠RQS = 33.5°
EXPLANATION
As we can see in the diagram, RQ is the diameter of circle P. Angles RPS and QPS are supplementary angles, so if m∠QPS = 113°, then,
[tex]m\angle RPS=180\degree-113\degree=67\degree[/tex]
Angle RPS is a central angle that intersects arc RS, so the measure of arc RS is also 67°.
We have to find the measure of angle RQS, which is an inscribed angle - note that the vertex is on the circle, and it intercepts arc RS, so its measure is half the measure of the intercepted arc,
[tex]m\angle RQS=\frac{1}{2}mRS=\frac{1}{2}\cdot67\degree=33.5\degree[/tex]
Hence, the measure of angle RQS is 33.5°.
