Answer :
To determine the angle between the hands of a clock at 2 o'clock, let's break down the process step by step.
1. Understand the Movement of the Hour Hand:
- A full rotation of the hour hand on a clock is 360 degrees and it takes 12 hours for a full cycle.
- Therefore, each hour mark represents a movement of [tex]\(\frac{360}{12} = 30\)[/tex] degrees.
- At 2 o'clock, the hour hand is at the 2-hour mark.
2. Position of the Hour Hand:
- The hour hand at the 2-hour mark: [tex]\(2 \times 30 = 60\)[/tex] degrees from the 12 o'clock position.
3. Understand the Movement of the Minute Hand:
- A full rotation of the minute hand on a clock is 360 degrees and it takes 60 minutes for a full cycle.
- Therefore, each minute mark represents a movement of [tex]\(\frac{360}{60} = 6\)[/tex] degrees.
- At 2 o'clock, the minute hand is at the 00-minute mark.
4. Position of the Minute Hand:
- The minute hand at the 00-minute mark: [tex]\(0 \times 6 = 0\)[/tex] degrees from the 12 o'clock position.
5. Calculate the Absolute Difference:
- The difference in positions between the hour hand and the minute hand: [tex]\(60 - 0 = 60\)[/tex] degrees.
6. Ensure the Angle is the Smallest Possible:
- Since the maximum possible angle between the hands of a clock is 360 degrees but we need the smallest angle which is less than or equal to 180 degrees.
- In our case, [tex]\(60\)[/tex] degrees is already less than 180 degrees.
Thus the angle between the hour and minute hands at 2 o'clock is [tex]\(60\)[/tex] degrees.
Since [tex]\(60\)[/tex] is not among the given options ([tex]\(28, 248, 308, 608, 728\)[/tex]), it seems there might be a typo or misunderstanding in the provided options. The correct angle, as calculated, is indeed 60 degrees.
Therefore, the answer, corrected for the actual calculation should be:
[tex]\(60\)[/tex] degrees, as derived from the correct analysis.
1. Understand the Movement of the Hour Hand:
- A full rotation of the hour hand on a clock is 360 degrees and it takes 12 hours for a full cycle.
- Therefore, each hour mark represents a movement of [tex]\(\frac{360}{12} = 30\)[/tex] degrees.
- At 2 o'clock, the hour hand is at the 2-hour mark.
2. Position of the Hour Hand:
- The hour hand at the 2-hour mark: [tex]\(2 \times 30 = 60\)[/tex] degrees from the 12 o'clock position.
3. Understand the Movement of the Minute Hand:
- A full rotation of the minute hand on a clock is 360 degrees and it takes 60 minutes for a full cycle.
- Therefore, each minute mark represents a movement of [tex]\(\frac{360}{60} = 6\)[/tex] degrees.
- At 2 o'clock, the minute hand is at the 00-minute mark.
4. Position of the Minute Hand:
- The minute hand at the 00-minute mark: [tex]\(0 \times 6 = 0\)[/tex] degrees from the 12 o'clock position.
5. Calculate the Absolute Difference:
- The difference in positions between the hour hand and the minute hand: [tex]\(60 - 0 = 60\)[/tex] degrees.
6. Ensure the Angle is the Smallest Possible:
- Since the maximum possible angle between the hands of a clock is 360 degrees but we need the smallest angle which is less than or equal to 180 degrees.
- In our case, [tex]\(60\)[/tex] degrees is already less than 180 degrees.
Thus the angle between the hour and minute hands at 2 o'clock is [tex]\(60\)[/tex] degrees.
Since [tex]\(60\)[/tex] is not among the given options ([tex]\(28, 248, 308, 608, 728\)[/tex]), it seems there might be a typo or misunderstanding in the provided options. The correct angle, as calculated, is indeed 60 degrees.
Therefore, the answer, corrected for the actual calculation should be:
[tex]\(60\)[/tex] degrees, as derived from the correct analysis.
