In the figure, VWXY is a parallelogram. O is the centre of the circle. Find
- ∠VYX
- ∠VWY
(a)
∠OWY = ∠WYO = 31° (Angle properties within a circle)
∠YOW
= 180° - 31° - 31°
= 118° (Angles sum of triangle)
∠OVW + ∠OWV = ∠WOY (Exterior angle of a triangle)
∠OVW = ∠OWV (Isosceles triangle, OV = OW)
∠OVW
= 118° ÷ 2
= 59° (Exterior angle of a triangle)
∠VYX
= 180° - 59°
= 121° (Interior angles)
(b)
∠VWY
= 180° - 59° - 31°
= 90° (Angle sum of triangles)
Answer(s): (a) 121°; (b) 90°