In the figure, O Is the centre of the circle and TY is parallel to UV. XZ = XY, ∠OUT = 55° and ∠ZYX = 53°. Find
- ∠VUA
- ∠UVX
(a)
OT = OU = Radius
∠TUO = ∠UTO = 55° (Isosceles triangle, OTB)
∠UOA
= 55° + 55°
= 110° (Exterior angle of a triangle)
OU = OA = Radius
∠OAU
= (180° - 110°) ÷ 2
= 70° ÷ 2
= 35°
∠VUA = 35° (Alternate angles, UV//TE)
(b)
XZ = XY
∠XYZ = ∠XZY = 53° (Isosceles triangle XYF)
∠YXZ
= 180° - 53° - 53°
= 74°
∠AXV = ∠YXZ = 74° (Vertically opposite angles)
∠UVX
= 180° - 74°
= 106° (Interior angles)
Answer(s): (a) 35°; (b) 106°