Question

ANSWER IS IN IMAGE! DO NOT NEED TO SHOW WORK!

Answer 1

m∠RQS = 33.5°

Step-by-step 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,

`m\angle RPS=180\degree-113\degree=67\degree`

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,

`m\angle RQS=(1)/(2)mRS=(1)/(2)\cdot67\degree=33.5\degree`

Hence, the measure of angle RQS is 33.5°.