Question 32
Angles and PolygonsIn the diagram, |SR| = |RQ| and ∠PRQ = 58°, ∠VQT = 19°. PQT, SQV and PSR are straight lines. Find ∠QPS.
- A.42°
- B.39°
- C.36°
- D.30°
Show the answer and explanation
Answer: A (42°)
Explanation
SR = RQ, so ∠RSQ = (180 − 58)/2 = 61°. ∠PQS = ∠VQT = 19° (vertically opposite). ∠RSQ is an exterior angle of triangle PQS, so ∠QPS = 61 − 19 = 42°.