In the figure, PQS is a triangle with QS = QP, while NPQR is a parallelogram and RQS is a straight line. Given ∠QRN = 92°, ∠MQS = 138° and ∠NMQ = 53°, find
- ∠QPS
- ∠MQP
(a)
∠NRQ
= ∠PQS
= 92° (Corresponding angles)
∠QPS
= (180° - 92°) ÷ 2
= 44° (Isosceles triangle)
(b)
∠MQP
= 360° - 138° - 92°
= 130° (Angles at a point)
Answer(s): (a) 44°; (b) 130°