In the figure, WXZ is a triangle with XZ = XW, while VWXY is a parallelogram and YXZ is a straight line. Given ∠XYV = 96°, ∠UXZ = 153° and ∠VUX = 49°, find
- ∠XWZ
- ∠UXW
(a)
∠VYX
= ∠WXZ
= 96° (Corresponding angles)
∠XWZ
= (180° - 96°) ÷ 2
= 42° (Isosceles triangle)
(b)
∠UXW
= 360° - 153° - 96°
= 111° (Angles at a point)
Answer(s): (a) 42°; (b) 111°