Each interior angle of a polygon is `108^(@)`, How many sides does it have ?

Options

A. `8`
B. `6`
C. `5`
D. `7`

Answer

To find the number of sides of a polygon given that each interior angle is \(108^\circ\), we can use the formula for the interior angle of a 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. **Set up the equation**: Since we know the interior angle is \(108^\circ\), we can set up the equation:
\[ 108 = \frac{(n-2) \times 180}{n} \]

2. **Multiply both sides by \(n\)** to eliminate the fraction:
\[ 108n = (n-2) \times 180 \]

3. **Expand the right side**:
\[ 108n = 180n - 360 \]

4. **Rearrange the equation**: Move all terms involving \(n\) to one side:
\[ 108n - 180n = -360 \]
\[ -72n = -360 \]

5. **Divide both sides by \(-72\)** to solve for \(n\):
\[ n = \frac{360}{72} \]

6. **Calculate the value**:
\[ n = 5 \]

### Conclusion:
The polygon has **5 sides**.