In the given figure, I is the incenter of △ABC, BI when produced meets the circumcircle of △ABC at D. Given, ∠BAC = 55° and ∠ACB = 65°; calculate :

(i) ∠DCA,

(ii) ∠DAC,

(iii) ∠DCI,

(iv) ∠AIC.

In the given figure, AB = AC = CD and ∠ADC = 38°. Calculate :

(i) Angle ABC

(ii) Angle BEC

In the given figure, AOB is a diameter and DC is parallel to AB. If ∠CAB = x°; find (in terms of x) the values of :

(i) ∠COB,

(ii) ∠DOC,

(iii) ∠DAC,

(iv) ∠ADC.

In the given figure, PQ is the diameter of the circle whose center is O. Given, ∠ROS = 42°, calculate ∠RTS.