To determine the angle between the hour and minute hands of a clock at 2 PM, we can follow a straightforward calculation method based on the positions of the hands.
1. **Position of the Hour Hand:**
At 2 PM, the hour hand is pointing directly at the 2 on the clock. Each hour represents a 30-degree increment (as there are 360 degrees in a full circle and 12 hours on a clock). Therefore, at 2 PM, the hour hand is positioned at:
2 hours × 30 degrees/hour = 60 degrees
2. **Position of the Minute Hand:**
At 2 PM, the minute hand is pointing at the 12 on the clock, which corresponds to 0 degrees.
3. **Calculating the Angle Between the Hands:**
Now we can calculate the angle between the hour hand and the minute hand:
Angle = |Position of hour hand – Position of minute hand|
Angle = |60 degrees – 0 degrees| = 60 degrees
Thus, the angle between the hour and minute hands at 2 PM is 60 degrees.
In summary, when it is 2 PM, the hour hand and the minute hand of the clock form an angle of 60 degrees.