1. ABCD is a cyclic quadrilateral. The sides AD and AB are extended to E and F, respectively. If \(\angle\) CBF = 120°, then find the measure of \(\angle\) CDE.

2. In the cyclic quadrilateral ABCD, side BC is extended up to point E. If \(\angle BAD = 140^\circ\), then find the value of \(\angle DCE\).

(a) 75° (b) 90° (c) 140° (d) None of the above

3. ABCD is a cyclic quadrilateral, and CD is extended up to point E. If \(\angle\)ADE = 92°, then what is the measure of \(\angle\)ABC?

(a) 88\(^o\) (b) 29\(^o\) (c) 92\(^o\) (d) 60\(^o\)

4. AB is extended to point X in the cyclic quadrilateral ABCD. If \(\angle\)XBC = 98° and \(\angle\)ADB = 45°, then what is the measure of \(\angle\)BAC?

5. In a circle centered at O, AB is a diameter. ABCD is a cyclic quadrilateral. Given \(\angle\)ABC = 65° and \(\angle\)DAC = 40°, find the value of \(\angle\)BCD.

6. If the cyclic quadrilateral ABCD has its sides AB and DC extended to meet at point P, and sides AD and BC extended to meet at point Q, then given \(\angle\)ADC = 85° and \(\angle\)BPC = 40°, find the value of \(\angle\)CQD.

7. ABCD is a cyclic quadrilateral. If \(\angle\)ABC = 65° and \(\angle\)CAD = 40°, then find the value of \(\angle\)BCD.

(a) 70° (b) 25° (c) 115° (d) 90°

8. ABCD is a cyclic quadrilateral. If \(\angle\) BAD = 65°, \(\angle\) ABD = 70°, and \(\angle\) BDC = 45°, then find the value of \(\angle\) ACB.

9. ABCD is a cyclic quadrilateral. The angle bisectors of \(\angle\)DAB and \(\angle\)BCD intersect the circle at points X and Y respectively. If O is the center of the circle, find the value of \(\angle\)XOY.

10. ABCD is a cyclic quadrilateral with O as the center of the circle. Side DC is extended up to point P. If \(\angle BCP = 108^\circ\), calculate and write the measure of \(\angle BOD\).

11. In the cyclic quadrilateral ABCD, side AB is extended up to point X. If \(\angle\)XBC = 82° and \(\angle\)ADB = 47°, then what is the measure of \(\angle\)BAC?

(a) 45° (b) 45° (c) 35° (d) 60°

12. In a circle with center \(O\), \(\bar{AB}\) is a diameter. On the opposite side of the circumference from the diameter \(\bar{AB}\), there are two points \(C\) and \(D\) such that \(\angle AOC = 130°\) and \(\angle BDC = x°\). Find the value of \(x\).

(a) 25° (b) 50° (c) 60° (d) 65°

13. In a circle with center \(O\), \(AB\) is the diameter, and \(P\) is a point on the circle. If \(\angle AOP = 104°\), find the value of \(\angle BPO\).

(a) 54° (b) 72° (c) 36° (d) 27°

14. ABCD is a cyclic quadrilateral. The sides AB and DC are extended to meet at point P, and the sides AD and BC are extended to meet at point Q. If ∠ADC = 85° and ∠BPC = 40°, then find the measures of ∠BAD and ∠CQD.

15. ABCD is a cyclic quadrilateral. The side BA is extended up to point F. AE is drawn parallel to CD, and ∠ABC = 92°, ∠FAE = 20°. Find the measure of ∠BCD.

16. In a circle centered at O, ABCD is a cyclic quadrilateral. Given: \(\angle ABD = 50^\circ\), \(\angle CAD = 28^\circ\), and \(\angle ADB = 32^\circ\) Find the measure of \(\angle BCD\).

(a) 72° (b) 52° (c) 62° (d) 82°

17. ABCD is a cyclic quadrilateral and O is the center of the circle. Given: \(\angle COD = 130^\circ\), \(\angle BAC = 25^\circ\) Find the values of \(\angle BOC\) and \(\angle BCD\).

(a) 40\(^o\),90\(^o\) (b) 50\(^o\),90\(^o\) (c) 65\(^o\),50\(^o\) (d) None of the above

18. PQRS is a cyclic quadrilateral. PQ is the diameter of the circle, and if \(\angle\)PRS = 56°, then what is the value of \(\angle\)QPS?

19. O is the center of the circle, and AB is its diameter. ABCD is a cyclic quadrilateral. Given that \(\angle\)ABC = 65° and \(\angle\)DAC = 60°, find the measure of \(\angle\)BCD.

20. AOB is the diameter of a circle. AC and BD are two chords that intersect at point E. If \(\angle\)COD = 40°, find the value of \(\angle\)CED.

21. In the adjacent figure, O is the center of the circle, AC is the diameter, and chord DE is parallel to diameter AC. If \(\angle\)CBD = 60°, find the value of \(\angle\)CDE.

22. In the adjacent figure, QS is the bisector of \(\angle\)PQR. If \(\angle\)SQR = 35° and \(\angle\)PRQ = 32°, find the value of \(\angle\)QSR.

23. In the adjacent figure, O is the center of the circle and AB is the diameter. AB and CD are perpendicular to each other, and \(\angle\)ADC = 50°. Find the value of \(\angle\)CAD.

24. The adjacent cyclic quadrilateral ABCD has its sides AD and AB extended to points E and F, respectively. If \(\angle\)CBF = 120°, then calculate the value of \(\angle\)CDE.

25. ABCD is a cyclic quadrilateral. The side AB is extended up to point X, and it is measured that ∠XBC = 82° and ∠ADB = 47°; calculate and write the value of ∠BAC.

26. In the adjacent figure, ABCD is a cyclic quadrilateral. BA is extended to point F. AE ∥ CD, ∠ABC = 92°, and ∠FAE = 20°. Find the measure of ∠BCD.

(a) 20° (b) 88° (c) 108° (d) 72°

27. In a circle with center O, where BOC is the diameter and ABCD is a cyclic quadrilateral, if \(\angle ADC = 110^\circ\), then find the value of \(\angle ACB\).