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If the time is 1:50, what is the angle between the hour and minute hands?

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Question: If the time is 1:50, what is the angle between the hour and minute hands?

Options:

  1. 130 degrees
  2. 140 degrees
  3. 150 degrees
  4. 160 degrees

Correct Answer: 150 degrees

Solution: 

At 1:50, the hour hand is at 95 degrees (1 hour * 30 degrees + 50 minutes * 0.5 degrees) and the minute hand is at 300 degrees (50 minutes * 6 degrees). The angle between them is |95 - 300| = 205 degrees.

If the time is 1:50, what is the angle between the hour and minute hands?

Practice Questions

Q1
If the time is 1:50, what is the angle between the hour and minute hands?
  1. 130 degrees
  2. 140 degrees
  3. 150 degrees
  4. 160 degrees

Questions & Step-by-Step Solutions

If the time is 1:50, what is the angle between the hour and minute hands?
  • Step 1: Understand that the clock is divided into 12 hours, and each hour represents 30 degrees (360 degrees / 12 hours).
  • Step 2: Calculate the position of the hour hand. At 1:00, the hour hand is at 30 degrees (1 hour * 30 degrees).
  • Step 3: Since it is now 1:50, the hour hand has moved 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 50 minutes: 50 minutes * 0.5 degrees = 25 degrees.
  • Step 5: Add the initial position of the hour hand (30 degrees) to the additional movement (25 degrees): 30 degrees + 25 degrees = 55 degrees.
  • Step 6: Now calculate the position of the minute hand. Each minute represents 6 degrees (360 degrees / 60 minutes).
  • Step 7: For 50 minutes, the minute hand is at: 50 minutes * 6 degrees = 300 degrees.
  • Step 8: To find the angle between the hour and minute hands, subtract the smaller angle from the larger angle: |55 degrees - 300 degrees|.
  • Step 9: Calculate the absolute difference: |55 - 300| = 245 degrees.
  • Step 10: 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.
  • Clock Angles – Understanding how to calculate the angles between the hour and minute hands of a clock based on their positions.
  • Degree Calculation – Applying the formulas for determining the positions of the hour and minute hands in degrees.
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