In the figure, O Is the centre of the circle and UZ is parallel to VX. YA = YZ, ∠OVU = 56° and ∠AZY = 49°. Find
- ∠XVB
- ∠VXY
(a)
OU = OV = Radius
∠UVO = ∠VUO = 56° (Isosceles triangle, OUB)
∠VOB
= 56° + 56°
= 112° (Exterior angle of a triangle)
OV = OB = Radius
∠OBV
= (180° - 112°) ÷ 2
= 68° ÷ 2
= 34°
∠XVB = 34° (Alternate angles, VX//UE)
(b)
YA = YZ
∠YZA = ∠YAZ = 49° (Isosceles triangle YZF)
∠ZYA
= 180° - 49° - 49°
= 82°
∠BYX = ∠ZYA = 82° (Vertically opposite angles)
∠VXY
= 180° - 82°
= 98° (Interior angles)
Answer(s): (a) 34°; (b) 98°