Express the following angles in degrees : `(pi)/(6),(14)/(15)pi,(11)/(18)pi,(7)/(90)pi`

Answer

To convert the given angles from radians to degrees, we can use the formula:

\[ \text{Degrees} = \text{Radians} \times \left(\frac{180}{\pi}\right) \]

Let's apply this formula step by step for each angle.

### Step 1: Convert \(\frac{\pi}{6}\) to degrees
\[ \text{Degrees} = \frac{\pi}{6} \times \left(\frac{180}{\pi}\right) \]
The \(\pi\) cancels out:
\[ = \frac{180}{6} = 30 \text{ degrees} \]

### Step 2: Convert \(\frac{14\pi}{15}\) to degrees
\[ \text{Degrees} = \frac{14\pi}{15} \times \left(\frac{180}{\pi}\right) \]
The \(\pi\) cancels out:
\[ = \frac{14 \times 180}{15} \]
Calculating the multiplication:
\[ = \frac{2520}{15} = 168 \text{ degrees} \]

### Step 3: Convert \(\frac{11\pi}{18}\) to degrees
\[ \text{Degrees} = \frac{11\pi}{18} \times \left(\frac{180}{\pi}\right) \]
The \(\pi\) cancels out:
\[ = \frac{11 \times 180}{18} \]
Calculating the multiplication:
\[ = \frac{1980}{18} = 110 \text{ degrees} \]

### Step 4: Convert \(\frac{7\pi}{90}\) to degrees
\[ \text{Degrees} = \frac{7\pi}{90} \times \left(\frac{180}{\pi}\right) \]
The \(\pi\) cancels out:
\[ = \frac{7 \times 180}{90} \]
Calculating the multiplication:
\[ = \frac{1260}{90} = 14 \text{ degrees} \]

### Final Answers
The angles in degrees are:
1. \(\frac{\pi}{6} = 30\) degrees
2. \(\frac{14\pi}{15} = 168\) degrees
3. \(\frac{11\pi}{18} = 110\) degrees
4. \(\frac{7\pi}{90} = 14\) degrees

---