Question

The angle (in degrees) between the hour hand and the minute hand of a 12-hour clock showing 6:30 is ............ (round off to 1 decimal place)

Hint:

To calculate the angle between the clock hands, remember that each hour represents a 30° separation, and each minute represents a 6° separation.

Answer 1

Correct Answer: 14.9

Step 1: Calculate the angle at 6:00.
At 6:00, the hour hand is at the 6th hour mark, which corresponds to an angle of: \[ \text{Angle} = 30^\circ \times 6 = 180^\circ \]
Step 2: Calculate the position of the minute hand.
At 6:30, the minute hand is at the 6th minute mark, which is: \[ \text{Angle of minute hand} = 30^\circ \times 6 = 180^\circ \]
Step 3: Find the angle between the hands.
The angle between the hour and minute hand is the absolute difference between the angles: \[ |195^\circ - 180^\circ| = 15^\circ \] Thus, the angle between the hands at 6:30 is 135°.
Step 4: Conclusion.
Thus, the correct answer is \( \boxed{135^\circ} \).