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 = 49°, ∠TUS = 34° and ∠PSQ = 115°, find
- ∠k
- ∠n
- ∠m
(a)
∠TSU = ∠PSQ = 115° (Vertically opposite angles)
∠k
= 180° - 115° - 34°
= 31° (Angles sum of triangle)
(b)
∠n
= 180° - 31°
= 149° (Interior angles)
(c)
∠m
= 180° - 31° - 31° - 34°
= 97° (Angles sum of triangle)
Answer(s): (a) 31°; (b) 149°; (c) 97°