Question

What is the measure of ROQ?

Answer 1

So the arcRSQ is 280°, now, recall that a circle has a total of 360°, so if we subtract the arcRSQ from the circle, what's leftover is arcRQ, namely 360° - 280° = arcRQ = 80°.

well, arcs get their angle measurements from the central angle they're in, is just so happen that the central angle for arcRQ is the ∡ROQ, therefore the degrees for ∡ROQ are the same as for arcRQ.