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 = 117°, find
- ∠x
- ∠z
- ∠y
(a)
∠NMP = ∠JMK = 117° (Vertically opposite angles)
∠x
= 180° - 117° - 40°
= 23° (Angles sum of triangle)
(b)
∠z
= 180° - 23°
= 157° (Interior angles)
(c)
∠y
= 180° - 23° - 23° - 40°
= 94° (Angles sum of triangle)
Answer(s): (a) 23°; (b) 157°; (c) 94°