Neela's clock is broken. The minute hand rotates around the clock correctly, but the hour hand is stuck in the three o'clock position. Suppose Neela first looks at the clock when the hands are aligned, and it shows 3:15. She looks at the clock again and sees that the hour and minute hand of the clock form the angle measuring -105 degrees. How many degrees could the minute hand have rotated to reach its current position?(1 point) Responses -375° -375° -465° -465° -435° -435° -95°

Answer 1

-435°

To find the angle the minute hand has rotated to reach its current position, we start by finding the angle discrepancy between the hour and minute hands when they were aligned at 3:15. The hour hand would have moved 15 minutes past the 3 o'clock position, which is a total of 90 degrees (since the hour hand moves 360 degrees over 12 hours, so 30 degrees per hour).

Next, we are given that the angle between the hour and minute hands is -105 degrees at the second observation. Since the hour hand has not moved, the minute hand must have moved 105 degrees from the 3:15 position to reach this angle.

Therefore, the total degrees the minute hand has rotated from 3:15 to its current position is 90 (from alignment to 3:15) + 105 (from 3:15 to current position) = 195 degrees. Since the minute hand moves a full 360 degrees every hour, we take 360 - 195 = 165 degrees as the possible rotation for the minute hand.

However, it is important to note that there is an error in the given options as none of them exactly match the correct answer.