The figure, not drawn to scale, O is the centre of the circle and ZE // AD // BC. Find
- ∠YOB
- ∠YDO
(a)
∠EOA
= 180° - 102°
= 78° (Interior angles, ZE//AO)
∠OBD = ∠ODB = 30° (Isosceles triangle)
∠AOB
= 30° + 30°
= 60° (Exterior angle of a triangle)
∠YOB
= 78° + 60°
= 138°
(b)
∠DOB
= 180° - 30° -30°
= 120° (Isosceles triangle)
∠YOD
= 360° - 138° - 120°
= 102° (Angles at a point)
YO = OD = Radius
∠YDO
= (180° - 102°) ÷ 2
= 78° ÷ 2
= 39° (Isosceles triangle)
Answer(s): (a) 138°; (b) 39°