In the figure, O Is the centre of the circle and RV is parallel to ST. UX = UV, ∠OSR = 55° and ∠XVU = 55°. Find
- ∠TSY
- ∠STU
(a)
OR = OS = Radius
∠RSO = ∠SRO = 55° (Isosceles triangle, ORB)
∠SOY
= 55° + 55°
= 110° (Exterior angle of a triangle)
OS = OY = Radius
∠OYS
= (180° - 110°) ÷ 2
= 70° ÷ 2
= 35°
∠TSY = 35° (Alternate angles, ST//RE)
(b)
UX = UV
∠UVX = ∠UXV = 55° (Isosceles triangle UVF)
∠VUX
= 180° - 55° - 55°
= 70°
∠YUT = ∠VUX = 70° (Vertically opposite angles)
∠STU
= 180° - 70°
= 110° (Interior angles)
Answer(s): (a) 35°; (b) 110°