Find the measure of each interior angle of a regular polygon having
(i) 10 sides (ii) 15 sides .

Answer

To find the measure of each interior angle of a regular polygon, we can use the formula:

\[ \text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n} \]

where \( n \) is the number of sides of the polygon.

### Step-by-Step Solution

#### (i) For a polygon with 10 sides:

1. **Identify the number of sides**: Here, \( n = 10 \).

2. **Substitute \( n \) into the formula**:
\[ \text{Interior Angle} = \frac{(10 - 2) \times 180^\circ}{10} \]

3. **Calculate \( (10 - 2) \)**:
\[ 10 - 2 = 8 \]

4. **Multiply by 180 degrees**:
\[ 8 \times 180^\circ = 1440^\circ \]

5. **Divide by the number of sides (10)**:
\[ \frac{1440^\circ}{10} = 144^\circ \]

Thus, the measure of each interior angle of a regular polygon with 10 sides is **144 degrees**.

#### (ii) For a polygon with 15 sides:

1. **Identify the number of sides**: Here, \( n = 15 \).

2. **Substitute \( n \) into the formula**:
\[ \text{Interior Angle} = \frac{(15 - 2) \times 180^\circ}{15} \]

3. **Calculate \( (15 - 2) \)**:
\[ 15 - 2 = 13 \]

4. **Multiply by 180 degrees**:
\[ 13 \times 180^\circ = 2340^\circ \]

5. **Divide by the number of sides (15)**:
\[ \frac{2340^\circ}{15} = 156^\circ \]

Thus, the measure of each interior angle of a regular polygon with 15 sides is **156 degrees**.

### Final Answers:
- For 10 sides: **144 degrees**
- For 15 sides: **156 degrees**