In the figure, MNQ is a triangle with NQ = NM, while LMNP is a parallelogram and PNQ is a straight line. Given ∠NPL = 94°, ∠KNQ = 143° and ∠LKN = 50°, find
- ∠NMQ
- ∠KNM
(a)
∠LPN
= ∠MNQ
= 94° (Corresponding angles)
∠NMQ
= (180° - 94°) ÷ 2
= 43° (Isosceles triangle)
(b)
∠KNM
= 360° - 143° - 94°
= 123° (Angles at a point)
Answer(s): (a) 43°; (b) 123°