In the given figure, the straight lines AB and CD pass through the centre O of the circle. If ∠AOD = 75° and ∠OCE = 40°, find :

(i) ∠CDE

(ii) ∠OBE.

In the adjoining figure, AB = AC = CD and ∠ADC = 35°. Calculate :

(i) ∠ABC

(ii) ∠BEC

In the given figure, O is the centre of the circle. If QR = OP and ∠ORP = 20°, find the value of x giving reasons.

In the given figure, I is the incentre of Δ ABC. Here AI produced meets the circumcircle of Δ ABC at D. If ∠ABC = 55° and ∠ACB = 65°, calculate :

(i) ∠BCD

(ii) ∠CBD

(iii) ∠DCI

(iv) ∠BIC