In the figure, O Is the centre of the circle and RV is parallel to ST. UX = UV, ∠OSR = 52° and ∠XVU = 50°. Find
- ∠TSY
- ∠STU
(a)
OR = OS = Radius
∠RSO = ∠SRO = 52° (Isosceles triangle, ORB)
∠SOY
= 52° + 52°
= 104° (Exterior angle of a triangle)
OS = OY = Radius
∠OYS
= (180° - 104°) ÷ 2
= 76° ÷ 2
= 38°
∠TSY = 38° (Alternate angles, ST//RE)
(b)
UX = UV
∠UVX = ∠UXV = 50° (Isosceles triangle UVF)
∠VUX
= 180° - 50° - 50°
= 80°
∠YUT = ∠VUX = 80° (Vertically opposite angles)
∠STU
= 180° - 80°
= 100° (Interior angles)
Answer(s): (a) 38°; (b) 100°
