This is **VERY FAMOUS** question and asked very frequently.

**Question**: At a given time (eg 8:15) what will the angle be between the minute and hour hands of an analog clock.

**Answer:** There are several methods to solve this problem but one method is by calculating the rate the angle changes every minute for each hand (hour,minute), find the angle compared to being 12 o’ clock for each hand and compute their absolute difference.

• In an analog clock the hour hand completes 360 degrees in 12 hours (720 minutes) so this is a rate of 0.5 degrees per minute or 30 degrees per hour.

• In an analog clock the minute hand completes 360 degrees in 1 hour (60 minutes) so this is a rate of 6 degrees per minute.

At 8:15

The hour hand would have moved 8×30+15×0.5=247.5 degrees from 12 o clock

The minute hand has moved away 15×6= 90 degrees from 12 o clock

Absolute Difference 247.5-90=157.5 degrees

At 7:45

The hour hand would have moved 7×30+45×0.5=232.5 degrees from 12 o clock

The minute hand has moved away 45×6= 270 degrees from 12 o clock

Absolute Difference 270-232.5=37.5 degrees