The sum of the interior angles of a polygon is 1620°. The number· of sides of the polygon are:

Options

A. 9
B. 11
C. 15
D. 12

Answer

To find the number of sides of a polygon given that the sum of its interior angles is 1620°, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**:
The formula for the sum of the interior angles of a polygon with \( N \) sides is:
\[ \text{Sum of interior angles} = (N - 2) \times 180° \]

2. **Set Up the Equation**:
We know from the problem that the sum of the interior angles is 1620°. Therefore, we can set up the equation:
\[ (N - 2) \times 180° = 1620° \]

3. **Solve for \( N - 2 \)**:
To isolate \( N - 2 \), divide both sides of the equation by 180°:
\[ N - 2 = \frac{1620°}{180°} \]

4. **Calculate the Right Side**:
Now, perform the division:
\[ N - 2 = 9 \]

5. **Solve for \( N \)**:
To find \( N \), add 2 to both sides:
\[ N = 9 + 2 = 11 \]

6. **Conclusion**:
Therefore, the number of sides of the polygon is \( N = 11 \).

### Final Answer:
The number of sides of the polygon is **11**.

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