In the figure, O Is the centre of the circle and SX is parallel to TU. VY = VX, ∠OTS = 55° and ∠YXV = 57°. Find
- ∠UTZ
- ∠TUV
(a)
OS = OT = Radius
∠STO = ∠TSO = 55° (Isosceles triangle, OSB)
∠TOZ
= 55° + 55°
= 110° (Exterior angle of a triangle)
OT = OZ = Radius
∠OZT
= (180° - 110°) ÷ 2
= 70° ÷ 2
= 35°
∠UTZ = 35° (Alternate angles, TU//SE)
(b)
VY = VX
∠VXY = ∠VYX = 57° (Isosceles triangle VXF)
∠XVY
= 180° - 57° - 57°
= 66°
∠ZVU = ∠XVY = 66° (Vertically opposite angles)
∠TUV
= 180° - 66°
= 114° (Interior angles)
Answer(s): (a) 35°; (b) 114°