What is the degree measure of an angle that measures `(7pi) /(15)` radians ?

Options

A. `((360-7pi )/(15))^(@)`
B. `(180 -(7pi)/(15))^(@)`
C. `252 ^(@)`
D. `84 ^(@)`

Answer

To convert the angle from radians to degrees, we can follow these steps:

### Step 1: Write down the given angle in radians.
The angle given is \( \frac{7\pi}{15} \) radians.

### Step 2: Use the conversion formula.
To convert radians to degrees, we use the formula:
\[ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \]

### Step 3: Substitute the given angle into the formula.
Substituting \( \frac{7\pi}{15} \) into the formula gives:
\[ \text{Degrees} = \frac{7\pi}{15} \times \frac{180}{\pi} \]

### Step 4: Simplify the expression.
Notice that \( \pi \) in the numerator and denominator cancels out:
\[ \text{Degrees} = \frac{7 \times 180}{15} \]

### Step 5: Calculate \( \frac{180}{15} \).
Now, we simplify \( \frac{180}{15} \):
\[ \frac{180}{15} = 12 \]
So, we have:
\[ \text{Degrees} = 7 \times 12 \]

### Step 6: Multiply to find the degree measure.
Calculating \( 7 \times 12 \):
\[ \text{Degrees} = 84 \]

### Final Answer:
The degree measure of the angle is \( 84^\circ \).

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