MNPQ is a quadrilateral and OMQP is a trapezium in which OM // QP and ∠NMQ = 112°, ∠MQP = 120°, ∠NPQ = 64° and QP = QM. Find
- ∠MNO
- ∠QMO
- ∠MPQ.
(a)
∠MNO
= 360° - 120° -112° - 64°
= 64° (Sum of angles in a quadrilateral)
(b)
∠QMO
= 180° - 120°
= 60° (Interior angles, MO//QC)
(c)
∠MPQ
= (180° - 120°) ÷ 2
= 60 ÷ 2
= 30° (Isosceles triangle)
Answer(s): (a) 64°; (b) 60°; (c) 30°