If an interior of a regular polygon is `170^(@)`, then the number of sides of the polygon is

Options

A. 36
B. 20
C. 18
D. 27

Answer

To find the number of sides of a regular polygon given that its interior angle is \(170^\circ\), we can use the formula for the interior angle of a regular 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**:
Given that the interior angle is \(170^\circ\), we can set up the equation:
\[ 170 = \frac{(n-2) \times 180}{n} \]

2. **Multiply both sides by \(n\)**:
To eliminate the fraction, multiply both sides by \(n\):
\[ 170n = (n-2) \times 180 \]

3. **Expand the right side**:
Distributing \(180\) on the right side gives:
\[ 170n = 180n - 360 \]

4. **Rearrange the equation**:
Move all terms involving \(n\) to one side and constant terms to the other side:
\[ 170n - 180n = -360 \]
This simplifies to:
\[ -10n = -360 \]

5. **Solve for \(n\)**:
Divide both sides by \(-10\):
\[ n = \frac{360}{10} = 36 \]

6. **Conclusion**:
Therefore, the number of sides of the polygon is \(36\).

### Final Answer:
The number of sides of the polygon is \(36\).