In the figure, HJK is parallel to NPQ and the line NK cuts ∠JNQ into half. Given that KN and JP are straight lines, ∠HJN = 50°, ∠NPM = 42° and ∠JMK = 114°, find
- ∠k
- ∠n
- ∠m
(a)
∠NMP = ∠JMK = 114° (Vertically opposite angles)
∠k
= 180° - 114° - 42°
= 24° (Angles sum of triangle)
(b)
∠n
= 180° - 24°
= 156° (Interior angles)
(c)
∠m
= 180° - 24° - 24° - 42°
= 88° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 156°; (c) 88°