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 = 40° and ∠PSQ = 118°, find
- ∠d
- ∠f
- ∠e
(a)
∠TSU = ∠PSQ = 118° (Vertically opposite angles)
∠d
= 180° - 118° - 40°
= 22° (Angles sum of triangle)
(b)
∠f
= 180° - 22°
= 158° (Interior angles)
(c)
∠e
= 180° - 22° - 22° - 40°
= 95° (Angles sum of triangle)
Answer(s): (a) 22°; (b) 158°; (c) 95°