Find the degree measure corresponding to the following measaure (Use `pi =(22)/(7)`),
(i)`(11)/(16)` (ii)`(7pi)/(6)`

Answer

To find the degree measure corresponding to the given radian measures, we will use the relationship that \( \pi \) radians is equal to \( 180^\circ \). We will also use \( \pi = \frac{22}{7} \) as given in the question.

### Part (i): Convert \( \frac{11}{16} \) to degrees

1. **Set up the conversion**:
\[ \text{Degrees} = \frac{11}{16} \times \left( \frac{180}{\pi} \right) \]
Since \( \pi = \frac{22}{7} \), we can substitute this value in:
\[ \text{Degrees} = \frac{11}{16} \times \left( \frac{180}{\frac{22}{7}} \right) \]

2. **Simplify the fraction**:
\[ \frac{180}{\frac{22}{7}} = 180 \times \frac{7}{22} = \frac{180 \times 7}{22} = \frac{1260}{22} \]
Now, we simplify \( \frac{1260}{22} \):
\[ \frac{1260}{22} = \frac{630}{11} \]

3. **Substituting back into the equation**:
\[ \text{Degrees} = \frac{11}{16} \times \frac{630}{11} \]
The \( 11 \) cancels out:
\[ \text{Degrees} = \frac{630}{16} \]

4. **Perform the division**:
\[ \frac{630}{16} = 39.375 \]
To express this in degrees and minutes:
\[ 39.375 = 39^\circ + 0.375 \times 60' = 39^\circ + 22.5' = 39^\circ 22.5' \]

Thus, the degree measure corresponding to \( \frac{11}{16} \) is \( 39^\circ 22.5' \).

### Part (ii): Convert \( \frac{7\pi}{6} \) to degrees

1. **Set up the conversion**:
\[ \text{Degrees} = \frac{7\pi}{6} \times \left( \frac{180}{\pi} \right) \]

2. **Cancel \( \pi \)**:
\[ \text{Degrees} = \frac{7 \times 180}{6} \]

3. **Simplify the fraction**:
\[ \frac{7 \times 180}{6} = 7 \times 30 = 210 \]

Thus, the degree measure corresponding to \( \frac{7\pi}{6} \) is \( 210^\circ \).

### Summary of Answers:
- (i) \( \frac{11}{16} \) radians = \( 39^\circ 22.5' \)
- (ii) \( \frac{7\pi}{6} \) radians = \( 210^\circ \)