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 = 48°, ∠RSQ = 39° and ∠MQN = 114°, find
- ∠q
- ∠s
- ∠r
(a)
∠RQS = ∠MQN = 114° (Vertically opposite angles)
∠q
= 180° - 114° - 39°
= 27° (Angles sum of triangle)
(b)
∠s
= 180° - 27°
= 153° (Interior angles)
(c)
∠r
= 180° - 27° - 27° - 39°
= 93° (Angles sum of triangle)
Answer(s): (a) 27°; (b) 153°; (c) 93°