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 = 47° and ∠TQU = 32°. Find
- ∠MQP
- ∠QSR
(a)
∠MQU
= (180° - 47°) ÷ 2
= 66.5° (Isosceles triangle)
∠MQP
= 180° - 66.5°
= 113.5° (Angles on a straight line)
(b)
∠SQR
= 66.5° - 32°
= 34.5°
∠QSR
= (180° - 34.5°) ÷ 2
= 72.75 ° (Isosceles triangle)
Answer(s): (a) 113.5°; (b) 72.75°