MNPQ is a quadrilateral and OMQP is a trapezium in which OM // QP and ∠NMQ = 108°, ∠MQP = 126°, ∠NPQ = 64° and QP = QM. Find
- ∠MNO
- ∠QMO
- ∠MPQ.
(a)
∠MNO
= 360° - 126° -108° - 64°
= 62° (Sum of angles in a quadrilateral)
(b)
∠QMO
= 180° - 126°
= 54° (Interior angles, MO//QC)
(c)
∠MPQ
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle)
Answer(s): (a) 62°; (b) 54°; (c) 27°