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 = 33° and ∠MQN = 115°, find
- ∠i
- ∠k
- ∠j
(a)
∠RQS = ∠MQN = 115° (Vertically opposite angles)
∠i
= 180° - 115° - 33°
= 32° (Angles sum of triangle)
(b)
∠k
= 180° - 32°
= 148° (Interior angles)
(c)
∠j
= 180° - 32° - 32° - 33°
= 99° (Angles sum of triangle)
Answer(s): (a) 32°; (b) 148°; (c) 99°