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 = 46°, ∠TUS = 35° and ∠PSQ = 117°, find
- ∠t
- ∠w
- ∠v
(a)
∠TSU = ∠PSQ = 117° (Vertically opposite angles)
∠t
= 180° - 117° - 35°
= 28° (Angles sum of triangle)
(b)
∠w
= 180° - 28°
= 152° (Interior angles)
(c)
∠v
= 180° - 28° - 28° - 35°
= 99° (Angles sum of triangle)
Answer(s): (a) 28°; (b) 152°; (c) 99°