In the figure, UVWX is a parallelogram. O is the centre of the circle. Find
- ∠UXW
- ∠UVX
(a)
∠OVX = ∠VXO = 30° (Angle properties within a circle)
∠XOV
= 180° - 30° - 30°
= 120° (Angles sum of triangle)
∠OUV + ∠OVU = ∠VOX (Exterior angle of a triangle)
∠OUV = ∠OVU (Isosceles triangle, OU = OV)
∠OUV
= 120° ÷ 2
= 60° (Exterior angle of a triangle)
∠UXW
= 180° - 60°
= 120° (Interior angles)
(b)
∠UVX
= 180° - 60° - 30°
= 90° (Angle sum of triangles)
Answer(s): (a) 120°; (b) 90°