In the figure, PQS is a triangle with QS = QP, while NPQR is a parallelogram and RQS is a straight line. Given ∠QRN = 100°, ∠MQS = 149° and ∠NMQ = 53°, find
- ∠QPS
- ∠MQP
(a)
∠NRQ
= ∠PQS
= 100° (Corresponding angles)
∠QPS
= (180° - 100°) ÷ 2
= 40° (Isosceles triangle)
(b)
∠MQP
= 360° - 149° - 100°
= 111° (Angles at a point)
Answer(s): (a) 40°; (b) 111°