Each interior angle of a polygon is `135^(@)`. How many sides does it have ?

Options

A. 8
B. 7
C. 6
D. 10

Answer

To find the number of sides of a polygon given that each interior angle is \(135^\circ\), we can use the formula for the interior angle of a polygon:

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

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 \(135^\circ\), we can set up the equation:
\[ 135 = \frac{(n - 2) \times 180}{n} \]

2. **Multiply both sides by \(n\)**: To eliminate the fraction, multiply both sides by \(n\):
\[ 135n = (n - 2) \times 180 \]

3. **Distribute on the right side**: Expand the right side of the equation:
\[ 135n = 180n - 360 \]

4. **Rearrange the equation**: Move all terms involving \(n\) to one side:
\[ 135n - 180n = -360 \]
This simplifies to:
\[ -45n = -360 \]

5. **Divide by -45**: To solve for \(n\), divide both sides by \(-45\):
\[ n = \frac{360}{45} \]

6. **Calculate \(n\)**: Perform the division:
\[ n = 8 \]

### Conclusion:
The polygon has **8 sides**.

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