In the figure, PQS is a triangle with QS = QP, while NPQR is a parallelogram and RQS is a straight line. Given ∠QRN = 98°, ∠MQS = 150° and ∠NMQ = 55°, find
- ∠QPS
- ∠MQP
(a)
∠NRQ
= ∠PQS
= 98° (Corresponding angles)
∠QPS
= (180° - 98°) ÷ 2
= 41° (Isosceles triangle)
(b)
∠MQP
= 360° - 150° - 98°
= 112° (Angles at a point)
Answer(s): (a) 41°; (b) 112°