Question

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

Answer 1

∠ABC = ∠ABD + ∠DBC = 30° + 30° = 60° 

In cyclic quadrilateral ABCD,

∠ADC = 180° - ABC = 180° - 60° = 120° 

(pair of opposite angles in a cyclic quadrilateral are supplementary)