1. If ABCD is a cyclic quadrilateral and \(\angle\)A=120°, what is the measure of \(\angle\)C ?
(a) \(\cfrac{π}{3}\) (b) \(\cfrac{π}{6}\) (c) \(\cfrac{π}{2}\) (d) \(\cfrac{2π}{3}\)
2. In the cyclic quadrilateral ABCD, if AB = AD, \(\angle\)DAC = 70° and \(\angle\)BDC = 50°, then what is the measure of \(\angle\)ACD?
(a) 30\(^o\) (b) 40\(^o\) (c) 50\(^o\) (d) 70\(^o\)
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. In the cyclic quadrilateral PQRS, the side PS is a diameter of the circle. If \(\angle\)PQR = 120°, then what is the measure of \(\angle\)SPR?
(a) 90° (b) 30° (c) 60° (d) 120°
5. ABCD is a cyclic quadrilateral. If ∠ ABD = 48°, what is the measure of ∠ ACD?
(a) 42° (b) 138° (c) 48° (d) 12°
6. In the cyclic quadrilateral PORS, the side PS is a diameter of the circle. If \(\angle\)PQR = 128°, then what is the measure of \(\angle\)SPR?
(a) 30° (b) 38° (c) 60° (d) None of the above
7. If ABCD is a cyclic parallelogram, then the measure of ∠A will be ——.
8. If the ratio of three consecutive angles of a cyclic quadrilateral is 1 : 2 : 3, what are the measures of the first and third angles?
9. If one angle of a cyclic quadrilateral is 75°, what is the measure of its opposite angle?
10. ABCD is a cyclic trapezium in which sides AD and BC are parallel to each other. If \(\angle\)ABC = 75°, then what is the measure of \(\angle\)BCD?
(a) 105° (b) 90° (c) 150° (d) 75°
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 ratio of three consecutive angles of a cyclic quadrilateral is 1:2:3, then what are the measures of the first and third angles?
13. In the cyclic quadrilateral ABCD, AB is the diameter and \(\angle\)ACD = 50°, then what is the measure of \(\angle\)BAD?
(a) 30° (b) 40° (c) 50° (d) 60°
14. 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°
15. ABCD is a cyclic trapezium in which sides AD and BC are parallel. If ∠ABC = 85°, then what is the measure of ∠BCD?
(a) 85° (b) 95° (c) 90° (d) 80°
16. ABCD is a cyclic quadrilateral and O is the center of the circle. If \(\angle\)COD = 120° and \(\angle\)BAC = 30°, then what is the measure of \(\angle\)BOC?
17. 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°
18. If PQRS is a cyclic parellelogram, what is the value of \( \angle P \) ?
(a) 45° (b) 60° (c) 90° (d) 75°
19. If ABCD is a cyclic quadrilateral and ∠A = 100°, then the measure of ∠C is—?
(a) 50° (b) 200° (c) 80° (d) 180°
20. The center of a circle is O, and AB is its diameter. ABCD is a cyclic quadrilateral. If \(\angle\)ABC = 65° and \(\angle\)DAC = 40°, then the measure of \(\angle\)BCD is—?
(a) 75° (b) 105° (c) 115° (d) 80°
21. ABCD is a cyclic trapezium, where AD \(\parallel\) BC. If \(\angle\)ABC = 70°, then the measure of \(\angle\)BCD will be—?
(a) 110° (b) 80° (c) 70° (d) 120°
22. If in parallelogram ABCD, \(\angle A - \angle D = 50^\circ\), then what is the measure of \(\angle C\)?
(a) 115\(^o\) (b) 110\(^o\) (c) 90\(^o\) (d) 65\(^o\)
23. "AB is a diameter of a circle with center O. P is any point on the circumference. If ∠ POA = 120°, then what is the measure of ∠ PBO?"
(a) 90\(^o\) (b) 60\(^o\) (c) 75\(^o\) (d) None of the above
24. The measure of a supplementary angle of a certain angle is four times the measure of its complementary angle. What is the measure of that angle?
(a) 30° (b) 60° (c) 45° (d) None of the above
25. If the measure of an angle in degrees is \(x\) and in radians is \(y\), then what is the value of \( \frac{x}{y} \)?
(a) \(\cfrac{π}{180}\) (b) \(\cfrac{π}{90}\) (c) \(\cfrac{90}{π}\) (d) \(\cfrac{180}{π}\)
26. If the circular (radian) measure of an angle is \( \frac{7\pi}{12} \), what is its value in the sexagesimal (degree) system?
(a) 90° (b) 105° (c) 135° (d) 160°
27. If two angles of a triangle are 75° and \( \frac{\pi^c}{6} \), then what is the measure of the third angle?
(a) 75° (b) 60° (c) 65° (d) 70°
28. The equilateral triangle XYZ is inscribed in a circle. If O is the center of the circle, what is the measure of \(\angle\)YOZ?
(a) 60° (b) 30° (c) 90° (d) 120°
29. In triangle ABC, AB = AC. A line drawn from point C intersects the extended line BA at point D. If AC = AD, what is the measure of \(\angle\)BCD in radians?
(a) \(\cfrac{π}{2}\) (b) \(π\) (c) \(\cfrac{π}{4}\) (d) \(\cfrac{π}{3}\)
30. In triangle ABC, the circumcenter is O; points A and B, C lie on opposite sides of the center. If \(\angle BOC = 120^\circ\), then what is the measure of \(\angle BAC\)?
(a) 50° (b) 60° (c) 70° (d) 80°
