1. The difference in measurement between two angles is 1°, and the sum of their radian measures is 1 radian. Express the angles in degrees.

2. 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°

3. 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.

4. What will be the measure of the third angle of a triangle in radians if the other two angles are \(65^\circ 56' 44''\) and \(64^\circ 3' 16''\)?

5. AC = CE ABC is an equilateral triangle BC = AC = CE ∠BCA = 60° ∠BCE = 180° − 60° = 120° BC = CE ∠CBE = ∠CEB = \(\frac{180° − 120°}{2} = 30°\) 180° = \(\pi\) radians 120° = \(\frac{\pi × 120}{180} = \frac{2\pi}{3}\) radians 30° = \(\frac{\pi × 30}{180} = \frac{\pi}{6}\) radians Angles of triangle ACE in radians: \(\frac{2\pi}{3}\), \(\frac{\pi}{6}\), \(\frac{\pi}{6}\)

6. **Give the definition of a radian. Prove that \(1^\circ < 1^c\)** (where \(1^c\) denotes 1 radian)

7. Express 18° in radians.

8. In a right-angled triangle, the difference between the two acute angles is \(\frac{2\pi}{5}\). Express the measures of these two angles in both radians and degrees.

9. In a right-angled triangle, the difference between the two acute angles is 30°. Express the measures of those two angles in both radians and degrees.

10. If the sum of two angles is 135° and their difference is \(\cfrac{\pi}{12}\), find the values of the two angles in degrees and radians.

11. 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.

12. In a triangle, one angle measures \(65^\circ\) and the second angle measures \(\cfrac{\pi}{12}\); calculate and write the measure of the third angle in both sexagesimal (degree-minute-second) and radian systems.

13. If the sum of two angles is 135° and their difference is \(\cfrac{\pi}{12}\), then calculate and write the measures of the two angles in both sexagesimal (degree-minute-second) and radian systems.

14. In the sexagesimal system, 1 radian is approximately equal to _________.

15. Write the circular (radian) measure of the angle produced by the tip of a clock’s hour hand after rotating for 1 hour.

16. If the ratio of three consecutive angles of a cyclic quadrilateral is 1:2:3, find the first and third angles in radians.

17. Find the radian measure of \( 67 \frac{1}{2}^\circ \).

18. If the angles of a triangle are in the ratio 1:2:3, find the radian measure of its largest angle.