A polygon has 9 sides . What is its interior angle ?
A. `140^(@)`
B. `100^(@)`
C. `120^(@)`
D. `40^(@)`

Options

A. D
B. A
C. B
D. C

Answer

To find the interior angle of a polygon with 9 sides, we can use the formula for the interior angle of a regular polygon:

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

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

### Step-by-step Solution:

1. **Identify the number of sides (n)**:
- The polygon has 9 sides, so \( n = 9 \).

2. **Substitute n into the formula**:
- Plugging \( n = 9 \) into the formula gives:
\[ \text{Interior Angle} = \frac{(9 - 2) \times 180}{9} \]

3. **Calculate \( (9 - 2) \)**:
- \( 9 - 2 = 7 \).

4. **Multiply by 180**:
- Now calculate \( 7 \times 180 \):
\[ 7 \times 180 = 1260 \]

5. **Divide by n (which is 9)**:
- Now divide \( 1260 \) by \( 9 \):
\[ \frac{1260}{9} = 140 \]

6. **Conclusion**:
- The interior angle of a polygon with 9 sides is \( 140^\circ \).

### Final Answer:
The correct answer is **A. \( 140^\circ \)**.