In the figure, JMQT is a rectangle, QRTU is a rhombus and MNPQ is a parallelogram. ∠QRT = 74° and ∠PQR = 92°.
- Find ∠LQM
- Find ∠QPN
(a)
∠TUQ = ∠TRQ = 74°
∠UQT
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠LQM
= 90° - 53°
= 37°
(b)
∠MQP
= 360° - 92° - 90° - 53°
= 125° (Angles at a point)
∠NPQ
= 180° - 125°
= 55° (Interior Angles, MQ//NF)
Answer(s): (a) 37°; (b) 55°