In the figure, O Is the centre of the circle and VA is parallel to XY. ZB = ZA, ∠OXV = 59° and ∠BAZ = 50°. Find
- ∠YXC
- ∠XYZ
(a)
OV = OX = Radius
∠VXO = ∠XVO = 59° (Isosceles triangle, OVB)
∠XOC
= 59° + 59°
= 118° (Exterior angle of a triangle)
OX = OC = Radius
∠OCX
= (180° - 118°) ÷ 2
= 62° ÷ 2
= 31°
∠YXC = 31° (Alternate angles, XY//VE)
(b)
ZB = ZA
∠ZAB = ∠ZBA = 50° (Isosceles triangle ZAF)
∠AZB
= 180° - 50° - 50°
= 80°
∠CZY = ∠AZB = 80° (Vertically opposite angles)
∠XYZ
= 180° - 80°
= 100° (Interior angles)
Answer(s): (a) 31°; (b) 100°