A clock shows 3:30. What is the smaller angle between the hour hand and the minute hand?

Answer and explanation

Correct answer: A. 75°

  1. Step 1: Calculate position of minute hand: At 30 minutes, minute hand is at 30 * 6° = 180° (pointing directly at 6).
  2. Step 2: Calculate position of hour hand: At 3:30, hour hand is at 3 30° + 30 0.5° = 90° + 15° = 105°.
  3. Step 3: Calculate angular difference: |180° - 105°| = 75°.
Answer
75°.
Why not the others: '90°' neglects the half-hour movement of the hour hand toward 4; '80°' miscalculates hour hand advance as 10°; '70°' miscalculates hour hand advance as 20°.

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