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If a clock shows 10:10, what is the angle between the hour and minute hand?

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Question: If a clock shows 10:10, what is the angle between the hour and minute hand?

Options:

  1. 35 degrees
  2. 50 degrees
  3. 60 degrees
  4. 75 degrees

Correct Answer: 75 degrees

Solution: 

At 10:10, the hour hand is at 85 degrees (10 hours * 30 degrees + 10 minutes * 0.5 degrees) and the minute hand is at 60 degrees (10 minutes * 6 degrees). The angle between them is |85 - 60| = 25 degrees.

If a clock shows 10:10, what is the angle between the hour and minute hand?

Practice Questions

Q1
If a clock shows 10:10, what is the angle between the hour and minute hand?
  1. 35 degrees
  2. 50 degrees
  3. 60 degrees
  4. 75 degrees

Questions & Step-by-Step Solutions

If a clock shows 10:10, what is the angle between the hour and minute hand?
  • Step 1: Understand that a clock has two hands: the hour hand and the minute hand.
  • Step 2: Know that the hour hand moves 30 degrees for each hour (360 degrees / 12 hours).
  • Step 3: Calculate the position of the hour hand at 10:10. First, find the degrees for 10 hours: 10 hours * 30 degrees = 300 degrees.
  • Step 4: The hour hand also moves as the minutes pass. It moves 0.5 degrees for each minute (30 degrees / 60 minutes). So for 10 minutes, it moves: 10 minutes * 0.5 degrees = 5 degrees.
  • Step 5: Add the two results from Step 3 and Step 4 to find the total position of the hour hand: 300 degrees + 5 degrees = 305 degrees.
  • Step 6: Now, calculate the position of the minute hand. The minute hand moves 6 degrees for each minute (360 degrees / 60 minutes). So for 10 minutes, it moves: 10 minutes * 6 degrees = 60 degrees.
  • Step 7: Find the angle between the hour hand and the minute hand by taking the absolute difference: |305 degrees - 60 degrees| = 245 degrees.
  • Step 8: Since angles on a clock can be measured in two ways, we can also find the smaller angle by subtracting from 360 degrees: 360 degrees - 245 degrees = 115 degrees.
  • Step 9: The final answer is the smaller angle, which is 115 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, with the hour hand moving additionally based on the minutes.
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