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 = 36° and ∠JMK = 116°, find
- ∠p
- ∠r
- ∠q
(a)
∠NMP = ∠JMK = 116° (Vertically opposite angles)
∠p
= 180° - 116° - 36°
= 28° (Angles sum of triangle)
(b)
∠r
= 180° - 28°
= 152° (Interior angles)
(c)
∠q
= 180° - 28° - 28° - 36°
= 94° (Angles sum of triangle)
Answer(s): (a) 28°; (b) 152°; (c) 94°