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 = 46°, ∠NPM = 40° and ∠JMK = 116°, find
- ∠e
- ∠g
- ∠f
(a)
∠NMP = ∠JMK = 116° (Vertically opposite angles)
∠e
= 180° - 116° - 40°
= 24° (Angles sum of triangle)
(b)
∠g
= 180° - 24°
= 156° (Interior angles)
(c)
∠f
= 180° - 24° - 24° - 40°
= 94° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 156°; (c) 94°