Teaser) what is the measure of the angle between the minute and the hour hands, when they show 3: 05 pm?

If it were 3:00 precisely then it would be 90 degrees.

The minute hand moves 360 degrees per hour so 5 minutes makes it 30 degrees closer to the hour haned.

The hour hand moves 360 degrees per 12 hours (720 minutes) so 5 minutes make it move 2.5 degrees further from the minute hand.

90 degrees -30 degrees + 2.5 degrees = 62.5 degrees

30° angle between the minute and the hour hands, when they show 3:05 PM.

Step-by-step explanation:

Given  : 3:05 PM

To find :  What is the measure of the angle between the minute and the hour hands.

Solution : We have given clock that showing time 3:05 PM

We know that clock make the complete angle that is 360 degree.

We know 1 hour = 60 minute.

So, angle formed by 60 minute  = 360 °.

Angle formed by 1 minute = .

Angle formed by 1 minute = 6°.

According to question :

At 3:05 pm

Total minute between minute hand and hour hand is 5.

So. Angle formed by 5 minute = 5 * 6 .

Angle formed by 5 minute = 30° .

Therefore, 30° angle between the minute and the hour hands, when they show 3:05 PM.