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 = 35° and ∠TWU = 117°, find
- ∠q
- ∠s
- ∠r
(a)
∠XWY = ∠TWU = 117° (Vertically opposite angles)
∠q
= 180° - 117° - 35°
= 28° (Angles sum of triangle)
(b)
∠s
= 180° - 28°
= 152° (Interior angles)
(c)
∠r
= 180° - 28° - 28° - 35°
= 100° (Angles sum of triangle)
Answer(s): (a) 28°; (b) 152°; (c) 100°