In the figure, O Is the centre of the circle and UZ is parallel to VX. YA = YZ, ∠OVU = 58° and ∠AZY = 51°. Find
- ∠XVB
- ∠VXY
(a)
OU = OV = Radius
∠UVO = ∠VUO = 58° (Isosceles triangle, OUB)
∠VOB
= 58° + 58°
= 116° (Exterior angle of a triangle)
OV = OB = Radius
∠OBV
= (180° - 116°) ÷ 2
= 64° ÷ 2
= 32°
∠XVB = 32° (Alternate angles, VX//UE)
(b)
YA = YZ
∠YZA = ∠YAZ = 51° (Isosceles triangle YZF)
∠ZYA
= 180° - 51° - 51°
= 78°
∠BYX = ∠ZYA = 78° (Vertically opposite angles)
∠VXY
= 180° - 78°
= 102° (Interior angles)
Answer(s): (a) 32°; (b) 102°
