In the figure, O Is the centre of the circle and VA is parallel to XY. ZB = ZA, ∠OXV = 54° and ∠BAZ = 55°. Find
- ∠YXC
- ∠XYZ
(a)
OV = OX = Radius
∠VXO = ∠XVO = 54° (Isosceles triangle, OVB)
∠XOC
= 54° + 54°
= 108° (Exterior angle of a triangle)
OX = OC = Radius
∠OCX
= (180° - 108°) ÷ 2
= 72° ÷ 2
= 36°
∠YXC = 36° (Alternate angles, XY//VE)
(b)
ZB = ZA
∠ZAB = ∠ZBA = 55° (Isosceles triangle ZAF)
∠AZB
= 180° - 55° - 55°
= 70°
∠CZY = ∠AZB = 70° (Vertically opposite angles)
∠XYZ
= 180° - 70°
= 110° (Interior angles)
Answer(s): (a) 36°; (b) 110°