Question

What is the angle between the hour hand and the minute hand when the time is 7:30?

• A. 23 degrees
• B. 43 degrees
• C. 45 degrees
• D. 54 degrees

Hint:

When calculating the angle between the clock hands, remember the minute hand moves 6 degrees per minute and the hour hand moves 0.5 degrees per minute.

Answer 1

The Correct Option is C

To find the angle between the hour and minute hands, we use the formula: \[ \text{Angle} = \left| 30H - \frac{11}{2}M \right| \] where \( H \) is the hour and \( M \) is the minute. For 7:30: - \( H = 7 \) - \( M = 30 \) Substituting into the formula: \[ \text{Angle} = \left| 30 \times 7 - \frac{11}{2} \times 30 \right| = \left| 210 - 165 \right| = \left| 45 \right| \] Thus, the angle between the hour and minute hands at 7:30 is **45 degrees**.

Answer 2

To find the angle between the hour and minute hands at 7:30, we follow a step-by-step calculation:

Step 1: Calculate the angle moved by the hour hand
Each hour mark represents 30 degrees (360° / 12 hours).
At 7:00, the hour hand is at: 7 × 30 = 210 degrees
At 7:30, the hour hand has moved an additional half-hour, which is:
30 minutes × 0.5° = 15 degrees (since the hour hand moves 0.5° per minute)
So at 7:30, the hour hand is at: 210 + 15 = 225 degrees

Step 2: Calculate the angle moved by the minute hand
The minute hand moves 6 degrees per minute (360° / 60 minutes).
At 30 minutes, the minute hand is at: 30 × 6 = 180 degrees

Step 3: Find the angle between the two hands
Angle = |225 - 180| = 45 degrees

Conclusion:
The angle between the hour and minute hands at 7:30 is 45 degrees.