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 = 45°, ∠UVT = 36° and ∠QTR = 114°, find
- ∠q
- ∠s
- ∠r
(a)
∠UTV = ∠QTR = 114° (Vertically opposite angles)
∠q
= 180° - 114° - 36°
= 30° (Angles sum of triangle)
(b)
∠s
= 180° - 30°
= 150° (Interior angles)
(c)
∠r
= 180° - 30° - 30° - 36°
= 99° (Angles sum of triangle)
Answer(s): (a) 30°; (b) 150°; (c) 99°