So this problem dropped in my mail today

Given a clock time in hh:mm format, determine, to the nearest degree, the angle between the hour and the minute hands.

# Hours

From a basic understanding of a clock we can say that every 3 hours is 90 degrees.Therefore every hour is 30 degrees.

To put this into an equation, "on the hour", the hour hand is at -

h * 30 degrees

**Example**: At 4 o'clock the hour hand is at 120 degrees

We have already established above that the hour hand moves **30 degree in an hour.**

An hour has **60 **minutes. Therefore every minute, the hour hand should move **0.5 degrees**.

**Example**-

At **4:15** the hour hand should have moved **7.5** degree from the 4 o'clock position.

120 + 7.5 = **127.5 degrees**

# Minutes

Converting minutes to angles is simple

There are 60 minutes. There are 360 degrees. Each minute is 6 degrees

**Example** - At **15 **minutes past the hour the minute hand is at **90 **degrees

15 * 6 = **90**

# Putting the two together

- Find the angle of the hour hand given the information above
- Find the angle of the minute hand given the information above
- Subtract the two angles taking into account whether we are measuring from hour to minute, or minute to hour.

**Example**- At

**4:15**, the degree between both hands is

**37.5 degrees**