What is the angle between the minute and hour hands of a clock at 4:20?

Problem restatement
Find the smaller angle between the hour and minute hands at 4:20.

Given data

• Hour hand speed = 0.5°/minute (30° per hour).
• Minute hand speed = 6°/minute (360° per hour).

Concept/Approach
At H:M, the angle is |30H − 5.5M| degrees (since 5.5 = 11/2).

Step-by-step calculation
Angle = |30×4 − 5.5×20| = |120 − 110| = 10°

Verification/Alternative
Direct positions: Hour hand at 4:20 is at 4×30° + 20×0.5° = 120° + 10° = 130°. Minute hand at 20 minutes is 20×6° = 120°. Difference = 10°.

Common pitfalls

• Using 30H − 6M (ignoring hour-hand movement during the minutes).

Final Answer
10°