What is the angle between hour hand and minute hand at 2:25 pm?

Options

A. `77.5^@`
B. `68^@`
C. `67.5^@`
D. none of these

Answer

To find the angle between the hour hand and the minute hand at 2:25 PM, we can use the formula for calculating the angle between the two hands of a clock:

**Step 1: Understand the formula**
The angle \( A \) between the hour hand and the minute hand can be calculated using the formula:
\[ A = |(30 \times h - (11/2) \times m)| \]
where \( h \) is the hour and \( m \) is the minutes.

**Step 2: Identify the values of h and m**
For the time 2:25 PM:
- \( h = 2 \)
- \( m = 25 \)

**Step 3: Substitute the values into the formula**
Now, substitute \( h \) and \( m \) into the formula:
\[ A = |(30 \times 2 - (11/2) \times 25)| \]

**Step 4: Calculate the hour hand position**
Calculate \( 30 \times 2 \):
\[ 30 \times 2 = 60 \]

**Step 5: Calculate the minute hand position**
Calculate \( (11/2) \times 25 \):
\[ (11/2) \times 25 = 11 \times 12.5 = 137.5 \]

**Step 6: Find the difference**
Now, substitute these values back into the equation:
\[ A = |60 - 137.5| = |-77.5| = 77.5 \]

**Step 7: Final angle calculation**
Since the angle must be less than 180 degrees, the angle between the hour hand and minute hand at 2:25 PM is:
\[ A = 77.5 \text{ degrees} \]

Thus, the angle between the hour hand and the minute hand at 2:25 PM is **77.5 degrees**.

---