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If a clock shows 4:20, what is the angle between the hour and minute hand?

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Question: If a clock shows 4:20, what is the angle between the hour and minute hand?

Options:

  1. 120 degrees
  2. 130 degrees
  3. 140 degrees
  4. 150 degrees

Correct Answer: 130 degrees

Solution: 

At 4:20, the hour hand is at 130 degrees (4 hours * 30 degrees + 20 minutes * 0.5 degrees) and the minute hand is at 120 degrees (20 minutes * 6 degrees). The angle between them is |130 - 120| = 10 degrees.

If a clock shows 4:20, what is the angle between the hour and minute hand?

Practice Questions

Q1
If a clock shows 4:20, what is the angle between the hour and minute hand?
  1. 120 degrees
  2. 130 degrees
  3. 140 degrees
  4. 150 degrees

Questions & Step-by-Step Solutions

If a clock shows 4:20, what is the angle between the hour and minute hand?
  • Step 1: Understand that a clock has 12 hours and each hour represents 30 degrees (360 degrees / 12 hours).
  • Step 2: Calculate the position of the hour hand. At 4:00, the hour hand is at 4 * 30 = 120 degrees.
  • Step 3: Since it's 20 minutes past 4, the hour hand moves further. Each minute, the hour hand moves 0.5 degrees (30 degrees / 60 minutes).
  • Step 4: Calculate the additional movement of the hour hand for 20 minutes: 20 minutes * 0.5 degrees = 10 degrees.
  • Step 5: Add the additional movement to the hour hand's position: 120 degrees + 10 degrees = 130 degrees.
  • Step 6: Calculate the position of the minute hand. Each minute represents 6 degrees (360 degrees / 60 minutes).
  • Step 7: For 20 minutes, the minute hand is at 20 minutes * 6 degrees = 120 degrees.
  • Step 8: Find the angle between the hour hand and the minute hand by taking the absolute difference: |130 degrees - 120 degrees| = 10 degrees.
  • Clock Angle Calculation – Understanding how to calculate the angles of the hour and minute hands based on their positions.
  • Degrees per Hour and Minute – Knowing that each hour represents 30 degrees and each minute represents 6 degrees, and how to apply these to find the angle.
  • Absolute Difference – Calculating the absolute difference between the two angles to find the angle between the hands.
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