What is the angle between minute and hour clock when the clock strikes 2:20?

Question

Accepted Answer

The angle between the minute and hour hands of a clock at 2:20 is 50 degrees.

Calculate the angle formed by the hour hand from 12 o'clock to the current time (2:20)
Calculate the angle formed by the minute hand from 12 o'clock to the current time (20 minutes past the hour)
Subtract the smaller angle from the larger angle to get the angle between the minute and hour hands

Accepted Answer

To find the angle between the minute and hour hands of a clock at 2:20, we can break down the problem into two parts:

### Step 1: Calculate the angle moved by the hour hand.
- The hour hand moves 30° per hour (360°/12 hours).
- At 2:00, the hour hand is at 60° (since 2 × 30° = 60°).
- By 2:20, the hour hand has moved further. Since the hour hand moves 0.5° per minute (30° per hour / 60 minutes), in 20 minutes, it will have moved 20 × 0.5° = 10°.
- Therefore, at 2:20, the hour hand is at 60° + 10° = 70°.

### Step 2: Calculate the angle moved by the minute hand.
- The minute hand moves 6° per minute (360°/60 minutes).
- At 20 minutes past the hour, the minute hand is at 20 × 6° = 120°.

### Step 3: Calculate the angle between the hands.
- The angle between the two hands is the difference between their positions: |120° - 70°| = 50°.

Final Answer:  
The angle between the minute and hour hands at 2:20 is **50 degrees**.

What is the angle between minute and hour clock when the clock strikes 2:20?

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