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 = 48°, ∠UVT = 35° and ∠QTR = 118°, find
- ∠i
- ∠k
- ∠j
(a)
∠UTV = ∠QTR = 118° (Vertically opposite angles)
∠i
= 180° - 118° - 35°
= 27° (Angles sum of triangle)
(b)
∠k
= 180° - 27°
= 153° (Interior angles)
(c)
∠j
= 180° - 27° - 27° - 35°
= 97° (Angles sum of triangle)
Answer(s): (a) 27°; (b) 153°; (c) 97°