In the figure, VWXY is a parallelogram. O is the centre of the circle. Find
- ∠VYX
- ∠VWY
(a)
∠OWY = ∠WYO = 36° (Angle properties within a circle)
∠YOW
= 180° - 36° - 36°
= 108° (Angles sum of triangle)
∠OVW + ∠OWV = ∠WOY (Exterior angle of a triangle)
∠OVW = ∠OWV (Isosceles triangle, OV = OW)
∠OVW
= 108° ÷ 2
= 54° (Exterior angle of a triangle)
∠VYX
= 180° - 54°
= 126° (Interior angles)
(b)
∠VWY
= 180° - 54° - 36°
= 90° (Angle sum of triangles)
Answer(s): (a) 126°; (b) 90°