Answer:
∠ROQ=41.5°
Step-by-step explanation:
we know that
∠NOQ=∠NOP+∠POR+∠ROQ ------> equation A
∠POR=∠ROQ -----> equation B (given problem)
substitute equation B in equation A
∠NOQ=∠NOP+∠ROQ+∠ROQ
∠NOQ=∠NOP+2∠ROQ
we have
∠NOP=31°
∠NOQ=114°
substitute and solve for ∠ROQ
114°=31°+2∠ROQ
2∠ROQ=114°-31°
2∠ROQ=83°
∠ROQ=41.5°
