Answer
Part A:
Quadrant I
Part B:
Quadrant III
Work Step by Step
Quadrant I has angles $0^{o}$ through $90^{o}$
Quadrant II has angles $90^{o}$ through $180^{o}$
Quadrant III has angles $180^{o}$ through $270^{o}$
Quadrant IV has angles $270^{o}$ through $360^{o}$
Part A:
Quadrant I because $0^{o} \leq 8.3^{o} \leq 90^{o}$
Part B:
Quadrant III because $180^{o} \leq 257^{o}30' \leq 270^{o}$