1. 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°

2. 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.

3. In the cyclic quadrilateral ABCD, side AB is extended up to point P. If ∠CAB = 35° and ∠CBP = 82°, then what is the measure of ∠ADB?

(a) 47° (b) 55° (c) 35° (d) 60°

4. 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.

5. 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.

6. In the cyclic quadrilateral ABCD, the side \( AB \) is extended to point \( X \), forming \( \angle XBC = 82^\circ \) and \( \angle ADB = 47^\circ \). Find the measure of \( \angle BAC \).

7. 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.

8. 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\(^o\)

9. PQRS is a cyclic quadrilateral in which side QR is extended up to point T. If the measures of angles ∠SRQ and ∠SRT are in the ratio 4:5, then find the measures of ∠SPQ and ∠SRQ.

10. ABCD is a cyclic quadrilateral. Side AB is extended to point X. If \(\angle XBC = 82^\circ\) and \(\angle ADB = 47^\circ\), find the value of \(\angle BAC\).

11. 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?

12. 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.

13. ABCD is a cyclic quadrilateral in a circle, and the side AB is extended to X. If \(\angle\)XBC = 82° and \(\angle\)ADB = 47°, then \(\angle\)BAC = ?

(a) 45° (b) 15° (c) 35° (d) 60°

14. 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 \(\angle BOD\).

15. PQRS is a cyclic quadrilateral, and the sides PQ and SR are extended to meet at point T. The center of the circle is O; if ∠POQ = 110°, ∠QOR = 60°, and ∠ROS = 80°, then calculate and write the values of ∠RQS and ∠QTR.

16. 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°

17. In triangle \( \triangle ABC \), AC = BC and side BC is extended up to point D. If \( \angle ACD = 144^\circ \), then find the radian measure of each angle of triangle ABC.

18. 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

19. In the cyclic quadrilateral ABCD, the sides AB and AD are extended to E and F, respectively. If \(\angle\)CBE = 120°, find the measure of \(\angle\)CDF.

20. ABCD is a convex quadrilateral in which side AB is extended to X. If \(\angle\)XBC = 82° and \(\angle\)ADB = 47°, then what is \(\angle\)BAC?

21. 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.

22. When the sides AB and DC of a cyclic quadrilateral ABCD are extended, they meet at point P; and when sides AD and BC are extended, they meet at point Q. If \(\angle\)ADC = 85° and \(\angle\)BPC = 40°, then calculate the measures of \(\angle\)BAD and \(\angle\)CQD.