Math Problem Statement

At 5:30, what angle is formed between the hour hand and the minute hand of the clock?

Solution

The question in the image is in Gujarati and translates to:

"At 5:30, what angle is formed between the hour hand and the minute hand of the clock?"

Let's solve this.

Step-by-step explanation:

  1. Hour hand movement:

    • The hour hand moves 30 degrees for every hour (360°/12 hours).
    • At 5:30, the hour hand is halfway between 5 and 6, so its position is: 5×30+(3060)×30=150+15=1655 \times 30 + \left(\frac{30}{60}\right) \times 30 = 150 + 15 = 165^\circ So, the hour hand is at 165 degrees from the 12 o'clock position.
  2. Minute hand movement:

    • The minute hand moves 6 degrees per minute (360°/60 minutes).
    • At 30 minutes, the minute hand is at: 30×6=18030 \times 6 = 180^\circ So, the minute hand is at 180 degrees from the 12 o'clock position.
  3. Angle between the hour and minute hand:

    • The angle between the two hands is the difference between their positions: 180165=15|180^\circ - 165^\circ| = 15^\circ

Thus, the angle between the hour hand and the minute hand at 5:30 is 15 degrees.

The correct answer is option D) 15°.

Let me know if you need further details!

Here are five related questions to expand on this:

  1. What is the angle between the hands of the clock at 4:20?
  2. How many degrees does the hour hand move per minute?
  3. What is the smallest angle between the hands of a clock at 3:15?
  4. How can we calculate the angle if the time is not exact, such as 7:45?
  5. What is the reflex angle between the hands at 2:00?

Tip: The formula for finding the angle between the hands of a clock at any given time is:
Angle=30H5.5M\text{Angle} = \left|30H - 5.5M\right|
where HH is the hour, and MM is the minutes.

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Math Problem Analysis

Mathematical Concepts

Geometry
Clock Angles

Formulas

Hour hand movement: 30 degrees per hour
Minute hand movement: 6 degrees per minute
Angle between hands: |30H - 5.5M|

Theorems

None (Basic clock angle problem)

Suitable Grade Level

Grades 6-8