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 = 41° and ∠PSQ = 117°, find
- ∠v
- ∠x
- ∠w
(a)
∠TSU = ∠PSQ = 117° (Vertically opposite angles)
∠v
= 180° - 117° - 41°
= 22° (Angles sum of triangle)
(b)
∠x
= 180° - 22°
= 158° (Interior angles)
(c)
∠w
= 180° - 22° - 22° - 41°
= 94° (Angles sum of triangle)
Answer(s): (a) 22°; (b) 158°; (c) 94°