In the figure, STUV is a parallelogram. O is the centre of the circle. Find
- ∠SVU
- ∠STV
(a)
∠OTV = ∠TVO = 33° (Angle properties within a circle)
∠VOT
= 180° - 33° - 33°
= 114° (Angles sum of triangle)
∠OST + ∠OTS = ∠TOV (Exterior angle of a triangle)
∠OST = ∠OTS (Isosceles triangle, OS = OT)
∠OST
= 114° ÷ 2
= 57° (Exterior angle of a triangle)
∠SVU
= 180° - 57°
= 123° (Interior angles)
(b)
∠STV
= 180° - 57° - 33°
= 90° (Angle sum of triangles)
Answer(s): (a) 123°; (b) 90°