The sum of the interior angles of a polygon is `1260^(@)`. The number of sides of the polygon is :

Options

A. 6
B. 7
C. 8
D. 9

Answer

To find the number of sides of a polygon given that the sum of its interior angles is 1260 degrees, we can use the formula for the sum of 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:
\[ \text{Sum of interior angles} = (n - 2) \times 180 \]
Given that the sum of the interior angles is 1260 degrees, we can set up the equation:
\[ (n - 2) \times 180 = 1260 \]

**Step 2: Solve for \( n \).**
To isolate \( n \), first divide both sides of the equation by 180:
\[ n - 2 = \frac{1260}{180} \]
Calculating the right side:
\[ n - 2 = 7 \]
Now, add 2 to both sides to solve for \( n \):
\[ n = 7 + 2 = 9 \]

**Step 3: Conclusion.**
Thus, the number of sides of the polygon is:
\[ \boxed{9} \]

---