In the given figure, AB is a diameter of the circle with center O. DO is parallel to CB and ∠DCB = 120°. Calculate :

(i) ∠DAB,

(ii) ∠DBA,

(iii) ∠DBC,

(iv) ∠ADC.

Also, show that the △AOD is an equilateral triangle.

In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and ∠EAB = 63°. Calculate :

(i) ∠EBA,

(ii) ∠BCD.

In the given figure, AC is the diameter of the circle with center O. CD and BE are parallel. Angle ∠AOB = 80° and ∠ACE = 10°. Calculate :

(i) Angle BEC,

(ii) Angle BCD,

(iii) Angle CED.

In the given figure, AE is the diameter of the circle. Write down the numerical value of ∠ABC + ∠CDE. Give reasons for your answer.