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 = 48°, ∠TUS = 33° and ∠PSQ = 112°, find
- ∠x
- ∠z
- ∠y
(a)
∠TSU = ∠PSQ = 112° (Vertically opposite angles)
∠x
= 180° - 112° - 33°
= 35° (Angles sum of triangle)
(b)
∠z
= 180° - 35°
= 145° (Interior angles)
(c)
∠y
= 180° - 35° - 35° - 33°
= 99° (Angles sum of triangle)
Answer(s): (a) 35°; (b) 145°; (c) 99°