Final answer:
The measure of angle PCQ is 16 degrees, which is found by subtracting the measure of arc RS from the measure of arc PQ and taking the absolute value.
Step-by-step explanation:
In the context of a circle C, arc PQ measures 105 degrees and represents the angle at the center subtended by this arc. Similarly, arc RS measures 121 degrees. To find the measure of angle PCQ, one would subtract the measure of arc RS from the measure of arc PQ since these arcs are presumably on opposite sides of the circle, forming an exterior angle at point P. The calculation would be 105 degrees - 121 degrees, which results in -16 degrees. However, angles in a circle are positive by definition, so we take the absolute value, making the measure of angle PCQ 16 degrees (Option B).