Each interior angle of a regular polygon is `140^(@)`. The number sides is :

Options

A. 10
B. 9
C. 6
D. 9

Answer

To find the number of sides of a regular polygon given that each interior angle is \(140^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the interior angle of a regular polygon**:
The formula for the interior angle \(A\) of a regular polygon with \(n\) sides is given by:
\[ A = \frac{(n-2) \times 180}{n} \]
where \(n\) is the number of sides.

2. **Set up the equation**:
Since we know that each interior angle is \(140^\circ\), we can set up the equation:
\[ \frac{(n-2) \times 180}{n} = 140 \]

3. **Multiply both sides by \(n\)** to eliminate the fraction:
\[ (n-2) \times 180 = 140n \]

4. **Distribute \(180\) on the left side**:
\[ 180n - 360 = 140n \]

5. **Rearrange the equation**:
Move all terms involving \(n\) to one side:
\[ 180n - 140n = 360 \]
This simplifies to:
\[ 40n = 360 \]

6. **Solve for \(n\)**:
Divide both sides by \(40\):
\[ n = \frac{360}{40} = 9 \]

7. **Conclusion**:
The number of sides of the polygon is \(n = 9\).

### Final Answer:
The number of sides of the polygon is \(9\).

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