In the figure, O is the centre of the circle, ∠AOE = 150°, ∠DAO = 51°. Calculate the sizes of the angles CEB and OCE.

In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight sided polygon inscribed in the circle with centre O. Calculate the sizes of:
(i) ∠AOB, (ii) ∠ACB (iii) ∠ABC

The figure given below, shows a circle with centre O. Given: ∠ AOC = a and ∠ ABC = b.
1. Find the relationship between a and b.
2. Find the measure of angle OAB, if OABC is a parallelogram.

ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°; Calculate:
(i) ∠DAB, (ii) ∠BDC

If I is the incentre of triangle ABC and AI when produced meets the circumcircle of triangle ABC in point D. If ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠DBC

In a regular pentagon ABCDE, Inscribed in a circle; find ratio between angle EDA and angle ADC.

In the figure, given below, ABCD is a cyclic quadrilateral in which ∠BAD = 75°; ∠ABD = 58°
and ∠ADC = 77°. Find:
1. ∠BDC
2. ∠BCD
3. ∠BCA.

In the figure, given alongside, AB ∥ CD and O is the centre of the circle. If ∠ADC = 25°; find
the angle AEB give reasons in support of your answer.

Prove that:
the parallelogram, inscribed in a circle, is a rectangle.

In the given figure, AOC is a diameter and AC is parallel to ED. If ∠CBE = 64°, Calculate ∠DEC .