In the figure, LMN is parallel to RST and the line RN cuts ∠MRT into half. Given that NR and MS are straight lines, ∠LMR = 46°, ∠RSQ = 34° and ∠MQN = 118°, find
- ∠p
- ∠r
- ∠q
(a)
∠RQS = ∠MQN = 118° (Vertically opposite angles)
∠p
= 180° - 118° - 34°
= 28° (Angles sum of triangle)
(b)
∠r
= 180° - 28°
= 152° (Interior angles)
(c)
∠q
= 180° - 28° - 28° - 34°
= 100° (Angles sum of triangle)
Answer(s): (a) 28°; (b) 152°; (c) 100°