In the figure, O Is the centre of the circle and TY is parallel to UV. XZ = XY, ∠OUT = 54° and ∠ZYX = 52°. Find
- ∠VUA
- ∠UVX
(a)
OT = OU = Radius
∠TUO = ∠UTO = 54° (Isosceles triangle, OTB)
∠UOA
= 54° + 54°
= 108° (Exterior angle of a triangle)
OU = OA = Radius
∠OAU
= (180° - 108°) ÷ 2
= 72° ÷ 2
= 36°
∠VUA = 36° (Alternate angles, UV//TE)
(b)
XZ = XY
∠XYZ = ∠XZY = 52° (Isosceles triangle XYF)
∠YXZ
= 180° - 52° - 52°
= 76°
∠AXV = ∠YXZ = 76° (Vertically opposite angles)
∠UVX
= 180° - 76°
= 104° (Interior angles)
Answer(s): (a) 36°; (b) 104°
