In the figure, JMQT is a rectangle, QRTU is a rhombus and MNPQ is a parallelogram. ∠QRT = 76° and ∠PQR = 94°.
- Find ∠LQM
- Find ∠QPN
(a)
∠TUQ = ∠TRQ = 76°
∠UQT
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠LQM
= 90° - 52°
= 38°
(b)
∠MQP
= 360° - 94° - 90° - 52°
= 124° (Angles at a point)
∠NPQ
= 180° - 124°
= 56° (Interior Angles, MQ//NF)
Answer(s): (a) 38°; (b) 56°