In the figure, O Is the centre of the circle and SX is parallel to TU. VY = VX, ∠OTS = 57° and ∠YXV = 51°. Find
- ∠UTZ
- ∠TUV
(a)
OS = OT = Radius
∠STO = ∠TSO = 57° (Isosceles triangle, OSB)
∠TOZ
= 57° + 57°
= 114° (Exterior angle of a triangle)
OT = OZ = Radius
∠OZT
= (180° - 114°) ÷ 2
= 66° ÷ 2
= 33°
∠UTZ = 33° (Alternate angles, TU//SE)
(b)
VY = VX
∠VXY = ∠VYX = 51° (Isosceles triangle VXF)
∠XVY
= 180° - 51° - 51°
= 78°
∠ZVU = ∠XVY = 78° (Vertically opposite angles)
∠TUV
= 180° - 78°
= 102° (Interior angles)
Answer(s): (a) 33°; (b) 102°