If the sum of the interior angles of a regular polygon is `540^(@)` then how many sides does it have?

Options

A. 6
B. 8
C. 5
D. 9

Answer

To find the number of sides of a regular polygon given that the sum of its interior angles is 540 degrees, we can use the formula for the sum of the interior angles of a polygon:

**Step 1: Use the formula for the sum of interior angles.**
The formula for the sum of the interior angles of a polygon with \( n \) sides is given by:
\[ \text{Sum of interior angles} = (n - 2) \times 180 \]
We know from the problem that this sum is 540 degrees.

**Step 2: Set up the equation.**
We can set up the equation based on the given information:
\[ (n - 2) \times 180 = 540 \]

**Step 3: Solve for \( n - 2 \).**
To isolate \( n - 2 \), we divide both sides of the equation by 180:
\[ n - 2 = \frac{540}{180} \]

**Step 4: Simplify the right side.**
Calculating the right side gives:
\[ n - 2 = 3 \]

**Step 5: Solve for \( n \).**
Now, we add 2 to both sides to find \( n \):
\[ n = 3 + 2 = 5 \]

**Step 6: Conclusion.**
Thus, the number of sides of the polygon is \( n = 5 \). This means the polygon is a pentagon.

### Summary of Steps:
1. Use the formula for the sum of interior angles.
2. Set up the equation based on the given sum.
3. Solve for \( n - 2 \).
4. Simplify the equation.
5. Solve for \( n \).
6. Conclude the number of sides.