The clock time at which the hands of a clock forms an acute angle is 2 o'clock.

There are a total of 12 hours on a clock face, and the hour hand moves at a constant rate while the minute hand moves continuously. The angle between the hour and minute hands changes as time passes.

To determine the clock time at which the hands form an acute angle, we need to understand how the angles change throughout the day.

Explanation:

1. Understanding the movement of the hands:
- The hour hand takes 12 hours to complete a full rotation, moving at a rate of 30 degrees per hour (360 degrees divided by 12 hours).
- The minute hand takes 60 minutes to complete a full rotation, moving at a rate of 6 degrees per minute (360 degrees divided by 60 minutes).

2. Identifying acute angles:
- An acute angle is an angle that measures less than 90 degrees.
- In the case of a clock, an acute angle is formed when the hour and minute hands are relatively close to each other.

3. Analyzing the angles formed at different times:
- At 12 o'clock, the hour hand points directly at the 12 while the minute hand points at the 12 as well. This creates an angle of 0 degrees, which is not acute.
- As time progresses, the minute hand moves faster than the hour hand, causing the angle between them to increase.
- The angle between the hands will continue to increase until it reaches 180 degrees at 6 o'clock.
- After 6 o'clock, the angle between the hands starts decreasing again.

4. Determining the time for an acute angle:
- The first time when the angle between the hands is less than 90 degrees after 6 o'clock is 7:05.
- However, we are looking for the first time before 6 o'clock when the hands form an acute angle.
- The next opportunity for an acute angle is at 8 o'clock, where the angle between the hands is 60 degrees.
- The angle between the hands continues decreasing until it reaches 0 degrees at 12 o'clock again.

Conclusion:
Based on the analysis, the clock time at which the hands of a clock form an acute angle is 2 o'clock. At this time, the angle between the hour and minute hands is approximately 60 degrees, which is less than 90 degrees, fulfilling the condition for an acute angle.

At 2 o'clock minute hand is at 12 and hour hand is at 2

We know,

1 rotation = 360 deg

So, angle at 2 = 2/12 * 360 deg = 60 deg

Hence, acute angle and reflex angle = 60 deg

= 360 deg -acute angle = 360 deg - 60 deg = 300 deg .

I hope it is clear dude,