If the sum of the interior angles of a regular polygon be 1080 degree, the number of sides of the polygon is:

Options

A. a. 6
B. b. 8
C. c. 10
D. d.`15`

Answer

To find the number of sides of a regular polygon given that the sum of its interior angles is 1080 degrees, we can follow these steps:

### 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:
\[ \text{Sum of interior angles} = (n - 2) \times 180 \]
This formula tells us how to calculate the total interior angle sum based on the number of sides.

### Step 2: Set up the equation
We know from the problem that the sum of the interior angles is 1080 degrees. Therefore, we can set up the equation:
\[ (n - 2) \times 180 = 1080 \]

### Step 3: Solve for \( n \)
Now, we will solve for \( n \):
1. Divide both sides of the equation by 180:
\[ n - 2 = \frac{1080}{180} \]
2. Calculate the right side:
\[ n - 2 = 6 \]
3. Add 2 to both sides to isolate \( n \):
\[ n = 6 + 2 \]
\[ n = 8 \]

### Step 4: Conclusion
The number of sides of the polygon is \( n = 8 \).