What is the angle between the hour and minute hands at 8:30?

Problem restatementCompute the smaller angle between hands at 8:30.

Given data

• Hour-hand angle = 30° per hour + 0.5° per minute.
• Minute-hand angle = 6° per minute.

Concept/ApproachFind absolute difference of the two angular positions.

Step-by-Step calculationHour hand at 8:30: 8×30 + 0.5×30 = 240 + 15 = 255°Minute hand at 30: 30×6 = 180°Angle = |255 − 180| = 75°

Common pitfallsIgnoring the hour-hand's extra 0.5°/min during the half hour.