In the figure, MNPQ is a trapezium and MQRU is a rhombus. MQ is parallel to NP and QR = QS. UQP and QTS are straight lines. ∠QMU = 46° and ∠TQU = 25°. Find
- ∠MQP
- ∠QSR
(a)
∠MQU
= (180° - 46°) ÷ 2
= 67° (Isosceles triangle)
∠MQP
= 180° - 67°
= 113° (Angles on a straight line)
(b)
∠SQR
= 67° - 25°
= 42°
∠QSR
= (180° - 42°) ÷ 2
= 69 ° (Isosceles triangle)
Answer(s): (a) 113°; (b) 69°