1. The angle subtended by a segment of a circle greater than a semicircle is _____.
2. The radius of a circle is 28 cm. What is the radian measure of the central angle subtended by an arc of length 5.5 cm on this circle?
3. If the radius of a circle is 7 cm, then what will be the radian measure of the central angle subtended by an arc of length 5.5 cm?
4. The measure of all inscribed angles subtended by the same arc in a circle is equal.
5. The radius of a circle is 28 cm. Find the radian measure of the central angle subtended by an arc of length 5.5 cm.
6. The radius of a circle is 28 cm. What is the circular measure of the central angle subtended by an arc of length 5.5 cm in that circle?
7. The diameter of a circle is 28 cm. What is the radian measure of the central angle subtended by an arc of length 5.5 cm?
8. If the radius of a circle is 7 cm, then find the radian measure of the central angle subtended by an arc of length 5.5 cm.
9. If O is the circumcenter of an equilateral triangle, then the central angle subtended by any one of its sides is _____________.
10. If the radius of a circle is 6 cm, calculate and write the radian measure of the central angle subtended at the center by an arc of length 15 cm.
11. The radius of a circle is 28 cm. In this circle, calculate and write the radian measure of the central angle subtended by an arc of length 5.5 cm.
12. What is the radian measure of the angle swept by the tip of a clock’s minute hand in 1 hour?
(a) \(2\pi\) radians. (b) \(\cfrac{\pi}{2}\) radians. (c) \(\pi\) radians. (d) \(4\pi\) radians.
13. If the three angles of a triangle are in the ratio 2:3:4, then the measure of the largest angle in degrees is ________.
14. An angle subtended by a segment smaller than a semicircle is an obtuse angle.
15. If the central angle of a circle centered at point O is 300°, then the angle subtended at the circumference by the same arc will be 60°.
16. Prove that the central angle subtended by an arc of a circle is twice any inscribed angle subtended by the same arc.
17. The measure of all angles in a circular segment is ______.
18. The angle subtended by a segment smaller than a semicircle is — —.
19. An angle subtended by a larger segment of a circle is an acute angle compared to the angle subtended by a semicircular segment.
20. An inscribed angle subtended by the same arc is half of the central angle subtended by that arc.
21. \(\triangle\)PQR is an equilateral triangle, and its circumcircle is centered at \(O\). The measure of \(\angle POQ\) is _____.
22. If \(AC = BC\) in a triangle and \(AB^2 = 2AC^2\), then the measure of \(\angle C\) is _____.
(a) 30° (b) 45° (c) 60° (d) 90°
23. If \(AC = BC\) in a triangle and \(AB^2 = 2AC^2\), then the measure of \(\angle C\) is _____.
24. The circular measure of each interior angle of a regular hexagon is _____.
(a) \(\cfrac{\pi^c}{4}\) (b) \(\cfrac{\pi^c}{6}\) (c) \(\cfrac{\pi^c}{3}\) (d) \(\cfrac{2\pi^c}{3}\)
25. Prove that the central angle subtended by an arc of a circle is twice the inscribed angle subtended by the same arc.
26. Prove that the central angle subtended by an arc of a circle is twice the inscribed angle subtended by the same arc.
27. Prove that the angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the circumference.
28. The radian measure of the supplementary angle of \( \cfrac{3\pi}{8} \) is _____.
29. Prove that an angle subtended by a semicircle is a right angle.
30. The circular measure of the complementary angle of \(\frac{3\pi}{8}\) is _____.
