In the figure, MNPQ is a quadrilateral where ∠MNP = 129° and ∠NPQ = 118°. ∠PQR = 73° and NP = PQ. The point R on MQ is such that NR is parallel to PQ. Calculate
- ∠NQR
- ∠NMR
(a)
∠PQN
= (180° - 118°) ÷ 2
= 31° (Isosceles triangle)
∠NQR
= 73° - 31°
= 42°
(b)
∠NMR
= 360° - 118° - 73° - 129°
= 40° (Sum of angles in a quadrilateral)
Answer(s): (a) 42°; (b) 40°