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 = 43°, ∠UVT = 36° and ∠QTR = 110°, find
- ∠i
- ∠k
- ∠j
(a)
∠UTV = ∠QTR = 110° (Vertically opposite angles)
∠i
= 180° - 110° - 36°
= 34° (Angles sum of triangle)
(b)
∠k
= 180° - 34°
= 146° (Interior angles)
(c)
∠j
= 180° - 34° - 34° - 36°
= 101° (Angles sum of triangle)
Answer(s): (a) 34°; (b) 146°; (c) 101°