Find the degree measures corresponding to the following measures :
`(7pi)/(6)`

Answer

To convert the angle \( \frac{7\pi}{6} \) radians to degrees, we can follow these steps:

### Step 1: Understand the conversion factor
We know that:
\[ \pi \text{ radians} = 180^\circ \]
This means that to convert radians to degrees, we can use the conversion factor:
\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \]

### Step 2: Set up the conversion
To convert \( \frac{7\pi}{6} \) radians to degrees, we multiply by the conversion factor:
\[ \text{Degrees} = \frac{7\pi}{6} \times \frac{180}{\pi} \]

### Step 3: Simplify the expression
Now, we can simplify the expression:
1. Cancel \( \pi \) in the numerator and denominator:
\[ \frac{7 \times 180}{6} \]
2. Simplify \( \frac{180}{6} \):
\[ 180 \div 6 = 30 \]
3. Now multiply:
\[ 7 \times 30 = 210 \]

### Step 4: Conclusion
Thus, the angle \( \frac{7\pi}{6} \) radians is equal to:
\[ 210^\circ \]

### Final Answer:
\[ \frac{7\pi}{6} \text{ radians} = 210^\circ \]

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