In the figure, O Is the centre of the circle and TY is parallel to UV. XZ = XY, ∠OUT = 52° and ∠ZYX = 54°. Find
- ∠VUA
- ∠UVX
(a)
OT = OU = Radius
∠TUO = ∠UTO = 52° (Isosceles triangle, OTB)
∠UOA
= 52° + 52°
= 104° (Exterior angle of a triangle)
OU = OA = Radius
∠OAU
= (180° - 104°) ÷ 2
= 76° ÷ 2
= 38°
∠VUA = 38° (Alternate angles, UV//TE)
(b)
XZ = XY
∠XYZ = ∠XZY = 54° (Isosceles triangle XYF)
∠YXZ
= 180° - 54° - 54°
= 72°
∠AXV = ∠YXZ = 72° (Vertically opposite angles)
∠UVX
= 180° - 72°
= 108° (Interior angles)
Answer(s): (a) 38°; (b) 108°
