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

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

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*30 + 20*0.5) and the minute hand is at 120 degrees (20*6). The angle between them is |130 - 120| = 10 degrees.

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

Practice Questions

Q1
If a clock shows 4:20, what is the angle between the hour and minute hands?
  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 hands?
  • Step 1: Understand that the clock has two hands: the hour hand and the minute hand.
  • Step 2: Calculate the position of the hour hand. Each hour represents 30 degrees (360 degrees / 12 hours). At 4:00, the hour hand is at 4 * 30 = 120 degrees.
  • Step 3: Since it's 4:20, the hour hand moves further. It moves 0.5 degrees for each minute (30 degrees / 60 minutes). So, for 20 minutes, it moves 20 * 0.5 = 10 degrees.
  • Step 4: Add the movement of the hour hand to its position at 4:00. So, 120 degrees + 10 degrees = 130 degrees.
  • Step 5: Now, calculate the position of the minute hand. Each minute represents 6 degrees (360 degrees / 60 minutes). For 20 minutes, the minute hand is at 20 * 6 = 120 degrees.
  • Step 6: Find the angle between the hour hand and the minute hand. Subtract the smaller angle from the larger angle: |130 degrees - 120 degrees| = 10 degrees.
  • Clock Angles – Understanding how to calculate the angles between the hour and minute hands of a clock based on their positions.
  • Angle Calculation – Applying the formulas for determining the positions of the hour and minute hands to find the angle between them.
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