Angle between Hour and Minute Hands

Question: Find the angle between hour and minute hands when the time is 3.27.
Answer: 58.5
Solution:

1. First, find the angle at minute hand is, from 12'o clock
2. Next, find the angle of hour hand is, from 12'o clock
3. The difference between them is the answer.

Angle of minute hand from 12'o clock:

Minute hand is showing 27 minutes (see the question).

For 60 mins, the minute handle will move 360 degree.

So, for 1 min, how much degree it will move? 

((1 * 360)  / 60) => 6 degree.

So, for 27 mins, the minute handle will be at, 27 * 6 degrees from 12'o clock.

Which is, 162 degree.

Angle of hour hand from 12'o clock:

The angle between each hour is 30 degree.

So, at 3'o clock, the hour handle will be exactly at 90 degree (from 12'o clock).

Now, the time has past 27 mins from 3'o clock (see question).

So, we need to find the hour handle moves for each minute.

For 60 mins, the hour handle moves 30 degree.

So, for 1 min, the hour handles moves: 

((1* 30)/60) => 0.5 degree.

So, for 27 mins, the hour handle would have moved, 27 * 0.5 degree,

which is 13.5 degree.

So, the total degree of hour handle from 12'o clock => 90 + 13.5 degrees.

It is 103.5 degree.

The difference between minute handle and hour handle => 162 - 103.5 => 58.5 degree.

58.5 degree is the answer.

Simple formula: 30 * hours - 5.5 * mins

For same question (3:27) => (30 * 3) - (5.5 * 27) => 90 -  148.5 => -58.5 (degree don't have signs)