In the figure, JMQT is a rectangle, QRTU is a rhombus and MNPQ is a parallelogram. ∠QRT = 72° and ∠PQR = 97°.
- Find ∠LQM
- Find ∠QPN
(a)
∠TUQ = ∠TRQ = 72°
∠UQT
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠LQM
= 90° - 54°
= 36°
(b)
∠MQP
= 360° - 97° - 90° - 54°
= 119° (Angles at a point)
∠NPQ
= 180° - 119°
= 61° (Interior Angles, MQ//NF)
Answer(s): (a) 36°; (b) 61°