In the figure, O Is the centre of the circle and UZ is parallel to VX. YA = YZ, ∠OVU = 54° and ∠AZY = 53°. Find
- ∠XVB
- ∠VXY
(a)
OU = OV = Radius
∠UVO = ∠VUO = 54° (Isosceles triangle, OUB)
∠VOB
= 54° + 54°
= 108° (Exterior angle of a triangle)
OV = OB = Radius
∠OBV
= (180° - 108°) ÷ 2
= 72° ÷ 2
= 36°
∠XVB = 36° (Alternate angles, VX//UE)
(b)
YA = YZ
∠YZA = ∠YAZ = 53° (Isosceles triangle YZF)
∠ZYA
= 180° - 53° - 53°
= 74°
∠BYX = ∠ZYA = 74° (Vertically opposite angles)
∠VXY
= 180° - 74°
= 106° (Interior angles)
Answer(s): (a) 36°; (b) 106°