In the figure, WXYZ is a parallelogram. O is the centre of the circle. Find
- ∠WZY
- ∠WXZ
(a)
∠OXZ = ∠XZO = 36° (Angle properties within a circle)
∠ZOX
= 180° - 36° - 36°
= 108° (Angles sum of triangle)
∠OWX + ∠OXW = ∠XOZ (Exterior angle of a triangle)
∠OWX = ∠OXW (Isosceles triangle, OW = OX)
∠OWX
= 108° ÷ 2
= 54° (Exterior angle of a triangle)
∠WZY
= 180° - 54°
= 126° (Interior angles)
(b)
∠WXZ
= 180° - 54° - 36°
= 90° (Angle sum of triangles)
Answer(s): (a) 126°; (b) 90°