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 = 50°, ∠TUS = 35° and ∠PSQ = 116°, find
- ∠k
- ∠n
- ∠m
(a)
∠TSU = ∠PSQ = 116° (Vertically opposite angles)
∠k
= 180° - 116° - 35°
= 29° (Angles sum of triangle)
(b)
∠n
= 180° - 29°
= 151° (Interior angles)
(c)
∠m
= 180° - 29° - 29° - 35°
= 95° (Angles sum of triangle)
Answer(s): (a) 29°; (b) 151°; (c) 95°