In the figure, PQR is parallel to UVW and the line UR cuts ∠QUW into half. Given that RU and QV are straight lines, ∠PQU = 50°, ∠UVT = 40° and ∠QTR = 116°, find
- ∠i
- ∠k
- ∠j
(a)
∠UTV = ∠QTR = 116° (Vertically opposite angles)
∠i
= 180° - 116° - 40°
= 24° (Angles sum of triangle)
(b)
∠k
= 180° - 24°
= 156° (Interior angles)
(c)
∠j
= 180° - 24° - 24° - 40°
= 90° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 156°; (c) 90°