Question

AB is the diameter of the circle with centre O. OD is parallel to BC and  ∠ AOD = 60° ; calculate the numerical values of:  ∠ DBC 

Answer 1

∠BDA = 90°   (Angle in a semicircle)

Also, ∠OAD is equilateral (∴ ∠OAD = 60° )

∴ ∠ODB = 90° - ∠ODA = 90° - 60° = 30° 

Also, OD || BC

∴ ∠DBC = ∠ODB = 30° (Alternate angles)