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

Options

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

Answer

To find the number of sides of a polygon given that the sum of all interior angles is \(1440^\circ\), we can use the formula for the sum of 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 the sum of the interior angles is \(1440^\circ\). Therefore, we can set up the equation:

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

### Step 2: Divide both sides by \(180^\circ\)
To simplify the equation, divide both sides by \(180^\circ\):

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

### Step 3: Calculate the right side
Now, calculate \(\frac{1440}{180}\):

\[ \frac{1440}{180} = 8 \]

So, we have:

\[ n - 2 = 8 \]

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

\[ n = 8 + 2 = 10 \]

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