Question

when the time is 2:18, how many degrees are there in the acute angle between the minute hand and the hour hand on a clock?

Explanation:

Step1: Calculate the position of the hour - hand

The hour - hand moves 360 degrees in 12 hours, so it moves 30 degrees in 1 hour ($\frac{360}{12}=30$) and 0.5 degrees in 1 minute ($\frac{30}{60} = 0.5$). At 2:18, the hour - hand has moved 2 full hours plus 18 minutes. The position of the hour - hand is $2\times30+18\times0.5=60 + 9=69$ degrees.

Step2: Calculate the position of the minute - hand

The minute - hand moves 360 degrees in 60 minutes, so it moves 6 degrees in 1 minute ($\frac{360}{60}=6$). At 18 minutes, the position of the minute - hand is $18\times6 = 108$ degrees.

Step3: Calculate the angle between the hands

Subtract the position of the hour - hand from the position of the minute - hand: $108−69 = 39$ degrees.

Answer:

39