In the figure, NPQ is parallel to TUV and the line TQ cuts ∠PTV into half. Given that QT and PU are straight lines, ∠NPT = 45°, ∠TUS = 33° and ∠PSQ = 112°, find
- ∠q
- ∠s
- ∠r
(a)
∠TSU = ∠PSQ = 112° (Vertically opposite angles)
∠q
= 180° - 112° - 33°
= 35° (Angles sum of triangle)
(b)
∠s
= 180° - 35°
= 145° (Interior angles)
(c)
∠r
= 180° - 35° - 35° - 33°
= 102° (Angles sum of triangle)
Answer(s): (a) 35°; (b) 145°; (c) 102°