In the figure, BCDE is a parallelogram. O is the centre of the circle. Find
- ∠BED
- ∠BCE
(a)
∠OCE = ∠CEO = 27° (Angle properties within a circle)
∠EOC
= 180° - 27° - 27°
= 126° (Angles sum of triangle)
∠OBC + ∠OCB = ∠COE (Exterior angle of a triangle)
∠OBC = ∠OCB (Isosceles triangle, OB = OC)
∠OBC
= 126° ÷ 2
= 63° (Exterior angle of a triangle)
∠BED
= 180° - 63°
= 117° (Interior angles)
(b)
∠BCE
= 180° - 63° - 27°
= 90° (Angle sum of triangles)
Answer(s): (a) 117°; (b) 90°