In the figure, QRS is parallel to VWX and the line VS cuts ∠RVX into half. Given that SV and RW are straight lines, ∠QRV = 42°, ∠VWU = 38° and ∠RUS = 112°, find
- ∠j
- ∠m
- ∠k
(a)
∠VUW = ∠RUS = 112° (Vertically opposite angles)
∠j
= 180° - 112° - 38°
= 30° (Angles sum of triangle)
(b)
∠m
= 180° - 30°
= 150° (Interior angles)
(c)
∠k
= 180° - 30° - 30° - 38°
= 100° (Angles sum of triangle)
Answer(s): (a) 30°; (b) 150°; (c) 100°