In the figure, STUV is a parallelogram. O is the centre of the circle. Find
- ∠SVU
- ∠STV
(a)
∠OTV = ∠TVO = 38° (Angle properties within a circle)
∠VOT
= 180° - 38° - 38°
= 104° (Angles sum of triangle)
∠OST + ∠OTS = ∠TOV (Exterior angle of a triangle)
∠OST = ∠OTS (Isosceles triangle, OS = OT)
∠OST
= 104° ÷ 2
= 52° (Exterior angle of a triangle)
∠SVU
= 180° - 52°
= 128° (Interior angles)
(b)
∠STV
= 180° - 52° - 38°
= 90° (Angle sum of triangles)
Answer(s): (a) 128°; (b) 90°