In the figure, O Is the centre of the circle and RV is parallel to ST. UX = UV, ∠OSR = 59° and ∠XVU = 51°. Find
- ∠TSY
- ∠STU
(a)
OR = OS = Radius
∠RSO = ∠SRO = 59° (Isosceles triangle, ORB)
∠SOY
= 59° + 59°
= 118° (Exterior angle of a triangle)
OS = OY = Radius
∠OYS
= (180° - 118°) ÷ 2
= 62° ÷ 2
= 31°
∠TSY = 31° (Alternate angles, ST//RE)
(b)
UX = UV
∠UVX = ∠UXV = 51° (Isosceles triangle UVF)
∠VUX
= 180° - 51° - 51°
= 78°
∠YUT = ∠VUX = 78° (Vertically opposite angles)
∠STU
= 180° - 78°
= 102° (Interior angles)
Answer(s): (a) 31°; (b) 102°