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 = 48°, ∠NPM = 36° and ∠JMK = 114°, find
- ∠m
- ∠p
- ∠n
(a)
∠NMP = ∠JMK = 114° (Vertically opposite angles)
∠m
= 180° - 114° - 36°
= 30° (Angles sum of triangle)
(b)
∠p
= 180° - 30°
= 150° (Interior angles)
(c)
∠n
= 180° - 30° - 30° - 36°
= 96° (Angles sum of triangle)
Answer(s): (a) 30°; (b) 150°; (c) 96°