The sum of interior angle of a regular polygon is `1440^@` then the number of sides is

Options

A. 8
B. 10
C. 12
D. 6

Answer

To find the number of sides of a regular polygon given that the sum of its interior angles is 1440 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:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]

### Step 2: Set up the equation
Given that the sum of the interior angles is 1440 degrees, we can set up the equation:
\[ (n - 2) \times 180^\circ = 1440^\circ \]

### Step 3: Solve for \( n - 2 \)
To isolate \( n - 2 \), divide both sides of the equation by 180:
\[ n - 2 = \frac{1440^\circ}{180^\circ} \]

### Step 4: Calculate the right-hand side
Now, perform the division:
\[ n - 2 = 8 \]

### Step 5: Solve for \( n \)
To find \( n \), add 2 to both sides:
\[ n = 8 + 2 = 10 \]

### Conclusion
The number of sides of the polygon is \( n = 10 \).