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 = 37° and ∠PSQ = 112°, find
- ∠i
- ∠k
- ∠j
(a)
∠TSU = ∠PSQ = 112° (Vertically opposite angles)
∠i
= 180° - 112° - 37°
= 31° (Angles sum of triangle)
(b)
∠k
= 180° - 31°
= 149° (Interior angles)
(c)
∠j
= 180° - 31° - 31° - 37°
= 95° (Angles sum of triangle)
Answer(s): (a) 31°; (b) 149°; (c) 95°