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 = 46°, ∠VWU = 39° and ∠RUS = 114°, find
- ∠i
- ∠k
- ∠j
(a)
∠VUW = ∠RUS = 114° (Vertically opposite angles)
∠i
= 180° - 114° - 39°
= 27° (Angles sum of triangle)
(b)
∠k
= 180° - 27°
= 153° (Interior angles)
(c)
∠j
= 180° - 27° - 27° - 39°
= 95° (Angles sum of triangle)
Answer(s): (a) 27°; (b) 153°; (c) 95°