In the figure, STU is parallel to XYZ and the line XU cuts ∠TXZ into half. Given that UX and TY are straight lines, ∠STX = 45°, ∠XYW = 32° and ∠TWU = 114°, find
- ∠k
- ∠n
- ∠m
(a)
∠XWY = ∠TWU = 114° (Vertically opposite angles)
∠k
= 180° - 114° - 32°
= 34° (Angles sum of triangle)
(b)
∠n
= 180° - 34°
= 146° (Interior angles)
(c)
∠m
= 180° - 34° - 34° - 32°
= 103° (Angles sum of triangle)
Answer(s): (a) 34°; (b) 146°; (c) 103°