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 = 117°, find
- ∠v
- ∠x
- ∠w
(a)
∠UTV = ∠QTR = 117° (Vertically opposite angles)
∠v
= 180° - 117° - 36°
= 27° (Angles sum of triangle)
(b)
∠x
= 180° - 27°
= 153° (Interior angles)
(c)
∠w
= 180° - 27° - 27° - 36°
= 99° (Angles sum of triangle)
Answer(s): (a) 27°; (b) 153°; (c) 99°