In the figure, MNQ is a triangle with NQ = NM, while LMNP is a parallelogram and PNQ is a straight line. Given ∠NPL = 96°, ∠KNQ = 148° and ∠LKN = 51°, find
- ∠NMQ
- ∠KNM
(a)
∠LPN
= ∠MNQ
= 96° (Corresponding angles)
∠NMQ
= (180° - 96°) ÷ 2
= 42° (Isosceles triangle)
(b)
∠KNM
= 360° - 148° - 96°
= 116° (Angles at a point)
Answer(s): (a) 42°; (b) 116°