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 = 44°, ∠TUS = 37° and ∠PSQ = 120°, find
- ∠k
- ∠n
- ∠m
(a)
∠TSU = ∠PSQ = 120° (Vertically opposite angles)
∠k
= 180° - 120° - 37°
= 23° (Angles sum of triangle)
(b)
∠n
= 180° - 23°
= 157° (Interior angles)
(c)
∠m
= 180° - 23° - 23° - 37°
= 99° (Angles sum of triangle)
Answer(s): (a) 23°; (b) 157°; (c) 99°