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 = 32° and ∠JMK = 117°, find
- ∠p
- ∠r
- ∠q
(a)
∠NMP = ∠JMK = 117° (Vertically opposite angles)
∠p
= 180° - 117° - 32°
= 31° (Angles sum of triangle)
(b)
∠r
= 180° - 31°
= 149° (Interior angles)
(c)
∠q
= 180° - 31° - 31° - 32°
= 100° (Angles sum of triangle)
Answer(s): (a) 31°; (b) 149°; (c) 100°