In the figure, O Is the centre of the circle and VA is parallel to XY. ZB = ZA, ∠OXV = 55° and ∠BAZ = 50°. Find
- ∠YXC
- ∠XYZ
(a)
OV = OX = Radius
∠VXO = ∠XVO = 55° (Isosceles triangle, OVB)
∠XOC
= 55° + 55°
= 110° (Exterior angle of a triangle)
OX = OC = Radius
∠OCX
= (180° - 110°) ÷ 2
= 70° ÷ 2
= 35°
∠YXC = 35° (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) 35°; (b) 100°
