Question

At 2:48, what is the degree measure of the smaller angle formed by the hour and minute hands of a 12 hour clock?

Answer 1

The angle is 204 degree.

Explanation:

The angle turned by minute hand in 1 minute is 6 degree

The angle turned by the hour hand in 1 hour is

For the hour hand :

The angle turned in 1 hour = 360/12 = 30degree

At 2 : 00 , the angle covered = 30 x 2 = 60 degree

In each minute the hour hand moves = 30 degrees / hour x 1 hour/60 min

= 1/2 degree

So at 2: 48 the hour hand is at 2*30 + 48 * 1/2 = 84 degrees

For the minute hand:

In each minute it turns = 6 degrees

So, at 48 minutes the minute hand is at 48 x 6 = 288 degrees

So, the angle between them is 288 - 84 = 204 degrees

Answer 2

The smaller angle will be "156°".

Explanation:

According to the question,

Before 12, the minute hand at 48 minutes:

=
`60-48`

=
`12` (minutes to 12)

So,

=
`12 \ minutes+14 \ minutes`

=
`26 \ minutes`

hence,

The smaller angle will be:

=
`26* 6^(\circ) \ each`

=
`156^(\circ)`