The sum of interior angles of a polygon is `2160^(@)`. The number of sides of the polygon is

Options

A. 14
B. 12
C. 13
D. 15

Answer

To find the number of sides of a polygon given that the sum of its interior angles is \( 2160^\circ \), we can use the formula for the sum of the interior angles of a polygon:

\[ \text{Sum of interior angles} = 180(n - 2) \]

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

### Step-by-Step Solution:

1. **Set up the equation**: We know that the sum of the interior angles is \( 2160^\circ \). Therefore, we can write the equation:
\[ 180(n - 2) = 2160 \]

2. **Divide both sides by 180**: To simplify the equation, we divide both sides by \( 180 \):
\[ n - 2 = \frac{2160}{180} \]

3. **Calculate the right side**: Now, we perform the division:
\[ \frac{2160}{180} = 12 \]
So, we have:
\[ n - 2 = 12 \]

4. **Solve for \( n \)**: Now, we add \( 2 \) to both sides to find \( n \):
\[ n = 12 + 2 = 14 \]

5. **Conclusion**: Therefore, the number of sides of the polygon is \( 14 \).

### Final Answer:
The number of sides of the polygon is \( 14 \).