In the figure, O Is the centre of the circle and UZ is parallel to VX. YA = YZ, ∠OVU = 52° and ∠AZY = 55°. Find
- ∠XVB
- ∠VXY
(a)
OU = OV = Radius
∠UVO = ∠VUO = 52° (Isosceles triangle, OUB)
∠VOB
= 52° + 52°
= 104° (Exterior angle of a triangle)
OV = OB = Radius
∠OBV
= (180° - 104°) ÷ 2
= 76° ÷ 2
= 38°
∠XVB = 38° (Alternate angles, VX//UE)
(b)
YA = YZ
∠YZA = ∠YAZ = 55° (Isosceles triangle YZF)
∠ZYA
= 180° - 55° - 55°
= 70°
∠BYX = ∠ZYA = 70° (Vertically opposite angles)
∠VXY
= 180° - 70°
= 110° (Interior angles)
Answer(s): (a) 38°; (b) 110°