The figure, not drawn to scale, O is the centre of the circle and ZE // AD // BC. Find
- ∠YOB
- ∠YDO
(a)
∠EOA
= 180° - 96°
= 84° (Interior angles, ZE//AO)
∠OBD = ∠ODB = 29° (Isosceles triangle)
∠AOB
= 29° + 29°
= 58° (Exterior angle of a triangle)
∠YOB
= 84° + 58°
= 142°
(b)
∠DOB
= 180° - 29° -29°
= 122° (Isosceles triangle)
∠YOD
= 360° - 142° - 122°
= 96° (Angles at a point)
YO = OD = Radius
∠YDO
= (180° - 96°) ÷ 2
= 84° ÷ 2
= 42° (Isosceles triangle)
Answer(s): (a) 142°; (b) 42°