Question

What is the angle between hour and minute hand of a clock at 6.30?

• A. 5 degree
• B. 10 degree
• C. 15 degree
• D. 20 degree

Hint:

A common mistake at 6:30 is to think the hour hand is exactly on the 6 and the minute hand is exactly on the 6, making the angle 0°. Always remember that the hour hand moves continuously. In 30 minutes, it moves halfway from the 6 to the 7, which corresponds to \( 30 \times 0.5^\circ = 15^\circ \).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
We need to find the angle between the two hands of a clock at a specific time. We must consider that the hour hand also moves continuously, not just in jumps from one hour to the next.

Step 2: Key Formula or Approach
The formula to find the angle (\(\theta\)) between the hour hand and the minute hand is: \[ \theta = \left| 30H - \frac{11}{2}M \right| \] where H is the hour (6 in this case) and M is the minute (30 in this case).
Alternatively, we can calculate the position of each hand individually from the 12 o'clock mark.

Step 3: Detailed Explanation
Method 1: Using the Formula
H = 6, M = 30. \[ \theta = \left| 30(6) - \frac{11}{2}(30) \right| \] \[ \theta = \left| 180 - 11 \times 15 \right| \] \[ \theta = \left| 180 - 165 \right| \] \[ \theta = 15^\circ \] Method 2: Calculating Individual Hand Positions


Position of the Minute Hand: The minute hand moves 360° in 60 minutes, which is 6° per minute. At 30 minutes past the hour, its position is: \[ \text{Angle}_M = 30 \text{ minutes} \times 6^\circ/\text{minute} = 180^\circ \text{ from 12} \] (This means it is pointing directly at the 6).
Position of the Hour Hand: The hour hand moves 360° in 12 hours, which is 30° per hour or 0.5° per minute. At 6:30, it has moved past the 6. The total time from 12:00 is 6 hours and 30 minutes = 6.5 hours. \[ \text{Angle}_H = 6.5 \text{ hours} \times 30^\circ/\text{hour} = 195^\circ \text{ from 12} \]
Angle Between Hands: The difference between their positions. \[ \theta = |\text{Angle}_H - \text{Angle}_M| = |195^\circ - 180^\circ| = 15^\circ \]

Step 4: Final Answer
The angle between the hour and minute hand at 6:30 is 15 degrees. Therefore, option (C) is the correct answer.