Convert the angle start fraction, pi, divided by, 3, end fraction 3π​ radians to degrees.

1. Break Down the Problem

To convert an angle from radians to degrees, we can use the conversion factor that $180^\circ$ is equivalent to $\pi$ radians.

2. Relevant Concepts

The formula for converting radians to degrees is: $\text{Degrees} = \text{Radians} \times \left( \frac{180^\circ}{\pi} \right)$

3. Analysis and Detail

Let's apply the conversion factor to $\frac{3\pi}{1}$ radians:

1. Identify the radians: $\text{Radians} = 3\pi$

2. Substitute the value into the conversion formula: $\text{Degrees} = 3\pi \times \left( \frac{180^\circ}{\pi} \right)$

3. Simplify the expression: $\text{Degrees} = 3 \times 180^\circ = 540^\circ$

4. Verify and Summarize

The calculations show that $3\pi$ radians convert to $540^\circ$.

Final Answer

The angle $3\pi$ radians is equal to $540^\circ$.