In the figure, O Is the centre of the circle and UZ is parallel to VX. YA = YZ, ∠OVU = 60° and ∠AZY = 54°. Find
- ∠XVB
- ∠VXY
(a)
OU = OV = Radius
∠UVO = ∠VUO = 60° (Isosceles triangle, OUB)
∠VOB
= 60° + 60°
= 120° (Exterior angle of a triangle)
OV = OB = Radius
∠OBV
= (180° - 120°) ÷ 2
= 60° ÷ 2
= 30°
∠XVB = 30° (Alternate angles, VX//UE)
(b)
YA = YZ
∠YZA = ∠YAZ = 54° (Isosceles triangle YZF)
∠ZYA
= 180° - 54° - 54°
= 72°
∠BYX = ∠ZYA = 72° (Vertically opposite angles)
∠VXY
= 180° - 72°
= 108° (Interior angles)
Answer(s): (a) 30°; (b) 108°