1. The circular measure of each interior angle of a regular hexagon is –

(a) \(\cfrac{π}{3}\) (b) \(\cfrac{2π}{3}\) (c) \(\cfrac{π}{6}\) (d) \(\cfrac{π}{4}\)

2. The circular measure of each exterior angle of a regular hexagon is –

(a) \(\cfrac{π}{3}\) (b) \(\cfrac{2π}{3}\) (c) \(\cfrac{π}{6}\) (d) \(\cfrac{π}{4}\)

3. The central angle of each interior angle of a regular hexagon:

(a) \(\cfrac{π}{3}\) (b) \(\cfrac{2π}{3}\) (c) \(\cfrac{π}{6}\) (d) \(\cfrac{π}{4}\)

4. The measure of all angles in a circular segment is ______.

5. The circular measure of the complementary angle of \(\frac{3\pi}{8}\) is _____.

6. Two circles touch each other externally at point C. AB is a common tangent to both circles and touches the circles at points A and B, respectively. Find the measure of \(\angle\)ACB.

(a) 60° (b) 45° (c) 30° (d) 90°

7. Two circles touch each other externally at point \(C\). \(AB\) is a common tangent to the two circles, touching them at points \(A\) and \(B\), respectively. The measurement of \(\angle ACB\) is –

(a) 60° (b) 45° (c) 30° (d) 90°

8. 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°

9. If the three angles of a triangle are in the ratio 2:3:4, then the measure of the largest angle in degrees is ________.

10. In an equilateral triangle ABC, the base BC is extended to a point E such that CE = BC. A is joined to E to form triangle ACE. Find the circular (radian) measures of the angles of triangle ACE.

11. If the sum of two angles is 135° and their difference is \(\frac{π}{12}\), write the angles in sexagesimal and circular measure.

12. A rotating ray, starting from a certain position, rotates two full turns in the counterclockwise direction (opposite to the clock hands) and then produces an additional angle of 30°. What are the sexagesimal (degree) and circular (radian) measures of this angle?

13. If each side of an equilateral triangle is 4 cm, then the measurement of the triangle's height is —

(a) \(4\sqrt{3}\) cm (b) \(16\sqrt{3}\) cm (c) \(8\sqrt{3}\) cm (d) \(2\sqrt{3}\) cm

14. 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°

15. If the height and the base radius of a right circular cone are equal, then the measure of the cone's apex angle will be _____.

16. Draw an isosceles triangle with a base length of 5.2 cm and each of the equal sides measuring 7 cm. Then, construct the circumcircle of the triangle and measure the circumradius. (Only mark the construction steps).

17. \(\triangle\)PQR is an equilateral triangle, and its circumcircle is centered at \(O\). The measure of \(\angle POQ\) is _____.

18. 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°

19. 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°

20. If the difference between the measures of the two acute angles in a right-angled triangle is 10°, determine their circular measures.

21. The measure of an angle subtended by a semicircle is _____.

22. A rectangle has a length of \( a \) units and a breadth of \( b \) units. When the rectangle is wrapped to form a right circular cylinder, the circumference of the base of the cylinder is equal to the length of the rectangle. The lateral surface area of the cylinder will be _____.

23. The radian measure of the supplementary angle of \( \cfrac{3\pi}{8} \) is _____.

24. 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?

25. The sum of two angles is 135°, and their difference is \(\cfrac{\pi}{12}\). Determine the sexagesimal and circular measures of both angles.

26. If the sum of two angles is 135° and their difference is \(\frac{\pi^c}{12}\), find their sexagesimal and circular measures.

27. If the sum of two angles is 135° and their difference is \( \cfrac{\pi}{12} \), write the sexagesimal and circular measures of the two angles.

28. If the sum of two angles is 135° and their difference is \(\cfrac{π}{12}\), write their sexagesimal and circular measures.

29. If the sum of two angles is 135° and their difference is \(\cfrac{π}{12}\), write their sexagesimal and circular measures.

30. The English translation is: **"If the sum of two angles is 135° and their difference is \(\frac{\pi}{12}\), determine the angles in both sexagesimal and circular measure."**