The sum of all interior angles of a polygon is `1440^(@)`. The number of sides of the polygon is

Options

A. 8
B. 9
C. 10
D. 12

Answer

To find the number of sides of a polygon given that the sum of its interior angles is \(1440^\circ\), we can use the formula for the sum of the interior angles of a polygon:

\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]

where \(n\) is the number of sides of the polygon.

### Step 1: Set up the equation
We know that the sum of the interior angles is \(1440^\circ\). Therefore, we can set up the equation:

\[ (n - 2) \times 180 = 1440 \]

### Step 2: Solve for \(n - 2\)
To isolate \(n - 2\), we divide both sides of the equation by \(180\):

\[ n - 2 = \frac{1440}{180} \]

### Step 3: Simplify the right side
Now we simplify \(\frac{1440}{180}\):

1. First, we can cancel out the zeros:
\[ \frac{1440}{180} = \frac{144}{18} \]

2. Now we can simplify \(\frac{144}{18}\):
- \(144 \div 18 = 8\)

So, we have:

\[ n - 2 = 8 \]

### Step 4: Solve for \(n\)
Now, we add \(2\) to both sides to find \(n\):

\[ n = 8 + 2 = 10 \]

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