Question

What is the angle between the minute hand and the hour hand of a clock if they show time 05:10?​

Answer 1

Explanation:

Correct answer:

A analog clock is divided up into 12 sectors, based on the numbers 1–12. One sector represents 30 degrees (360/12 = 30). If the hour hand is directly on the 10, and the minute hand is on the 2, that means there are 4 sectors of 30 degrees between then, thus they are 120 degrees apart (30 * 4 = 120).

Answer 2

We know a minute hand takes 1 hour = 60 minutes to complete one revolution, i.e., to rotate about 360°.

• Angle rotated by the minute hand in 60 minutes = 360°

• Angle rotated by the minute hand in 1 minute = 360°/60 = 6°

So,

→   Angle rotated by the minute hand in 10 minutes = 6° × 10 = 60°

We know an hour hand takes 12 hours to complete one revolution, i.e., to rotate about 360°.

• Angle rotated by the hour hand in 12 hours = 360°

• Angle rotated by the hour hand in 1 hour or 60 minutes = 360°/12 = 30°

• Angle rotated by the hour hand in 1 minute = 30°/60 = 0.5°

So,

→   Angle rotated by the hour hand in 5 hours and 10 minutes = 5 × 30° + 10 × 0.5° = 155°

Now, the angle between the minute hand and the hour hand at time 05:10 = 155° - 60° = 95°