In the figure, O Is the centre of the circle and RV is parallel to ST. UX = UV, ∠OSR = 53° and ∠XVU = 53°. Find
- ∠TSY
- ∠STU
(a)
OR = OS = Radius
∠RSO = ∠SRO = 53° (Isosceles triangle, ORB)
∠SOY
= 53° + 53°
= 106° (Exterior angle of a triangle)
OS = OY = Radius
∠OYS
= (180° - 106°) ÷ 2
= 74° ÷ 2
= 37°
∠TSY = 37° (Alternate angles, ST//RE)
(b)
UX = UV
∠UVX = ∠UXV = 53° (Isosceles triangle UVF)
∠VUX
= 180° - 53° - 53°
= 74°
∠YUT = ∠VUX = 74° (Vertically opposite angles)
∠STU
= 180° - 74°
= 106° (Interior angles)
Answer(s): (a) 37°; (b) 106°