Step 1a

To find the angle between the hour and minute hands of the clock when the minute hand is pointing at 3 and the hour hand is pointing at 9, you can use the following formula:

Angle = \$(30\times "hours" - (11/2)\times "minutes")\$

Explanation: To find the angle between the hour and minute hands of a clock at 3:00 and 9:00, use

Angle = \$30 times "hours" - (11/2) times "minutes"\$. The angle for this time is 90 degrees.

Step 1b

Where : hour is the current hour on the clock, in this case, it’s 9.

minutes is the number of minutes past the last full hour, in this case, it’s 0 (since the minute hand is pointing at 3).

Explanation: In this step, the time is 9:00 and "minutes" represents the number of minutes that have passed since the last full hour, which is 0 in this case since the minute hand points to 3.

Step 1c

Using these values in the formula: Angle = \$(30\times 9 - (11/2)\times 0)\$ = 270 - 0 = 270 degrees.

So, the angle between the hour and minute hands of the clock is 270 degrees.

Explanation: As per the calculations performed, the angle between the hour and minute hands of the clock is determined to be 270 degrees.

Step 1d

Now, to find out how many degrees the minute hand moves in 15 minutes, you can use the fact that the minute hand of a clock moves 6 degrees for every minute.

Explanation: Calculate the position of the minute hand. It’s pointing at 3, which is 15 minutes on the clock.

Step 1e

Therefore, in 15 minutes, the minute hand will move: Degrees moved = \$((6 "degrees")/("minute")) \times 15 "minutes"\$ = 90 degrees.

So, the minute hand moves 90 degrees in 15 minutes.

Explanation: Therefore, in 15 minutes, the minute hand will move 90 degrees.