In the figure, STUV is a parallelogram. O is the centre of the circle. Find
- ∠SVU
- ∠STV
(a)
∠OTV = ∠TVO = 45° (Angle properties within a circle)
∠VOT
= 180° - 45° - 45°
= 90° (Angles sum of triangle)
∠OST + ∠OTS = ∠TOV (Exterior angle of a triangle)
∠OST = ∠OTS (Isosceles triangle, OS = OT)
∠OST
= 90° ÷ 2
= 45° (Exterior angle of a triangle)
∠SVU
= 180° - 45°
= 135° (Interior angles)
(b)
∠STV
= 180° - 45° - 45°
= 90° (Angle sum of triangles)
Answer(s): (a) 135°; (b) 90°