Question

At 3:20, what is the degree measure of the acute angle formed by the hour hand and the minute hand on a 12-hour analog clock?

Answer 1

Answer:

20 deg

Step-by-step explanation:

A 12-hour analog clock face has 12 hour markers in 360 degrees, so the angle between one hour and the the next hour is 30 deg.

At 3:00 the hour hand makes a 90 deg angle with the 12 marker.

At 4:00 the hour hand makes a 120 degree angle with the 12 marker.

At 3:20, the hour hand has gone 20/60 of the way from the 3 marker to the 4 marker, so it has gone 1/3 of the way from 90 degrees to 120 degrees with the 12 marker. 1/3 * 30 + 90 = 100 deg. The hour hand is making a 100-deg angle with the 12 marker.

At 3:20, the minutes hand is at the 4 marker, so it makes a 120-degree angle with the 12 marker.

The angle made by the hands is 120 deg = 10 deg = 20 deg.