In the figure, O Is the centre of the circle and RV is parallel to ST. UX = UV, ∠OSR = 54° and ∠XVU = 57°. Find
- ∠TSY
- ∠STU
(a)
OR = OS = Radius
∠RSO = ∠SRO = 54° (Isosceles triangle, ORB)
∠SOY
= 54° + 54°
= 108° (Exterior angle of a triangle)
OS = OY = Radius
∠OYS
= (180° - 108°) ÷ 2
= 72° ÷ 2
= 36°
∠TSY = 36° (Alternate angles, ST//RE)
(b)
UX = UV
∠UVX = ∠UXV = 57° (Isosceles triangle UVF)
∠VUX
= 180° - 57° - 57°
= 66°
∠YUT = ∠VUX = 66° (Vertically opposite angles)
∠STU
= 180° - 66°
= 114° (Interior angles)
Answer(s): (a) 36°; (b) 114°
