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 = 47°, ∠NPM = 32° and ∠JMK = 114°, find
- ∠x
- ∠z
- ∠y
(a)
∠NMP = ∠JMK = 114° (Vertically opposite angles)
∠x
= 180° - 114° - 32°
= 34° (Angles sum of triangle)
(b)
∠z
= 180° - 34°
= 146° (Interior angles)
(c)
∠y
= 180° - 34° - 34° - 32°
= 101° (Angles sum of triangle)
Answer(s): (a) 34°; (b) 146°; (c) 101°