Neela's clock is broken. The minute hand rotates around the clock correctly, but the hour hand is

Question

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)

-95°
-465°
-435°
-375°

Answer 1

To solve this problem, we can set up an equation to represent the angle between the hour and minute hands of the clock.

Let x be the number of degrees the minute hand has rotated from 12:00.

Since the hour hand is stuck at 3:00, we know that the hour hand has not moved at all. The angle between the hour and minute hands is 90 degrees when the hands are aligned (as they are at 3:15).

So, the angle between the hour and minute hands at 3:15 is 90 + x.

Given that the angle between the hour and minute hands at the second observation is -105 degrees, we set up the equation:

90 + x - 105 = -105

Simplify the equation:

90 + x - 105 = -105
x - 15 = -105
x = -105 + 15
x = -90

Therefore, the minute hand has rotated -90 degrees from the 12 o'clock position to reach its current position.

The answer is -90 degrees.