A clock that said 3 o'clock has moved its hands -2/3π radians. How many degrees did the hands of the clock moved?

1. Break Down the Problem

We need to convert the angle of rotation from radians to degrees. The hands of the clock originally point at 3 o'clock, and they have moved $-\frac{2}{3}\pi$ radians.

2. Relevant Concepts

To convert radians to degrees, we use the conversion factor: $1 \text{ radian} = \frac{180}{\pi} \text{ degrees}$

3. Analysis and Detail

We will convert the angle of $-\frac{2}{3}\pi$ radians to degrees using the formula mentioned above:

$\text{Degrees} = \text{Radians} \times \frac{180}{\pi}$

Substituting the value:

$\text{Degrees} = -\frac{2}{3}\pi \times \frac{180}{\pi}$

4. Verify and Summarize

Calculating that:

$\text{Degrees} = -\frac{2 \times 180}{3} = -\frac{360}{3} = -120$

This indicates that the hands of the clock moved $-120$ degrees.

Final Answer

The hands of the clock moved $-120$ degrees.