Answer:
arc RP = 84 degrees
Step-by-step explanation:
If the angle NPQ is 102 degrees, we can find the angle NPM:
NPM + NPQ = 180
NPM + 102 = 180
NPM = 78 degrees.
Now, with the triangle NPM, we can find the angle MNP:
60 + 78 + MNP = 180
MNP = 180 - 60 - 78 = 42 degrees
The angle MNP is inscribed in the circle, and is related to the arc RP:
arc RP = 2 * MNP
arc RP = 2 * 42 = 84 degrees
