MNPQ is a quadrilateral and OMQP is a trapezium in which OM // QP and ∠NMQ = 110°, ∠MQP = 128°, ∠NPQ = 65° and QP = QM. Find
- ∠MNO
- ∠QMO
- ∠MPQ.
(a)
∠MNO
= 360° - 128° -110° - 65°
= 57° (Sum of angles in a quadrilateral)
(b)
∠QMO
= 180° - 128°
= 52° (Interior angles, MO//QC)
(c)
∠MPQ
= (180° - 128°) ÷ 2
= 52 ÷ 2
= 26° (Isosceles triangle)
Answer(s): (a) 57°; (b) 52°; (c) 26°