Find the angle between the hour hand and the minute hand of a clock, when the…

Solution: Find the angle between the hour and minute hands at 3:25.

• Minute hand angle = 6 × minutes = 6 × 25 = 150°.

• Hour hand angle = 30 × hours + 0.5 × minutes = 30 × 3 + 0.5 × 25 = 90 + 12.5 = 102.5°.

• Angle between them = |150 − 102.5| = 47.5° which is 47½°.

Note: Always use minute-hand angle = 6 × minutes and hour-hand angle = 30 × hours + 0.5 × minutes. Common mistakes include treating the hour hand as fixed at the hour mark or using the position for a different minute value.