IF n is a constant equal to the number of degrees in an angle measuring `3pi` radians, what is the value of n?

Options

A. 240
B. 320
C. 270
D. 540

Answer

To find the value of \( n \), which represents the number of degrees in an angle measuring \( 3\pi \) radians, we will follow these steps:

### Step 1: Understand the conversion from radians to degrees
To convert radians to degrees, we use the conversion factor:
\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \]

### Step 2: Set up the conversion for \( 3\pi \) radians
We need to convert \( 3\pi \) radians into degrees. Using the conversion factor, we can express this as:
\[ n = 3\pi \times \frac{180}{\pi} \]

### Step 3: Simplify the expression
Now, we can simplify the expression:
\[ n = 3 \times 180 \]

### Step 4: Calculate the value of \( n \)
Now we perform the multiplication:
\[ n = 540 \]

### Conclusion
Thus, the value of \( n \) is:
\[ n = 540 \text{ degrees} \]

### Final Answer
The answer is \( n = 540 \).

---