In the figure, PQS is a triangle with QS = QP, while NPQR is a parallelogram and RQS is a straight line. Given ∠QRN = 94°, ∠MQS = 154° and ∠NMQ = 59°, find
- ∠QPS
- ∠MQP
(a)
∠NRQ
= ∠PQS
= 94° (Corresponding angles)
∠QPS
= (180° - 94°) ÷ 2
= 43° (Isosceles triangle)
(b)
∠MQP
= 360° - 154° - 94°
= 112° (Angles at a point)
Answer(s): (a) 43°; (b) 112°