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 = 37° and ∠TWU = 112°, find
- ∠q
- ∠s
- ∠r
(a)
∠XWY = ∠TWU = 112° (Vertically opposite angles)
∠q
= 180° - 112° - 37°
= 31° (Angles sum of triangle)
(b)
∠s
= 180° - 31°
= 149° (Interior angles)
(c)
∠r
= 180° - 31° - 31° - 37°
= 98° (Angles sum of triangle)
Answer(s): (a) 31°; (b) 149°; (c) 98°