If each interior angle of a regular polygon measures `140^(@)`, how many side does the polygon have?

Options

A. 5 sides
B. 6 sides
C. 9 sides
D. 10 sides

Answer

To find the number of sides of a regular polygon where each interior angle measures \(140^\circ\), we can follow these steps:

### Step 1: Understand the relationship between the number of sides and the interior angles.
Let \(n\) be the number of sides of the polygon. Since it is a regular polygon, all interior angles are equal.

### Step 2: Write the formula for the sum of interior angles.
The sum of the interior angles of a polygon with \(n\) sides is given by the formula:
\[ \text{Sum of interior angles} = 180(n - 2) \]

### Step 3: Express the sum of the interior angles in terms of \(n\).
Since each interior angle measures \(140^\circ\), the total sum of the interior angles can also be expressed as:
\[ \text{Sum of interior angles} = 140n \]

### Step 4: Set the two expressions for the sum of interior angles equal to each other.
Equating the two expressions we have:
\[ 180(n - 2) = 140n \]

### Step 5: Expand and simplify the equation.
Expanding the left side:
\[ 180n - 360 = 140n \]

### Step 6: Rearrange the equation to isolate \(n\).
Now, move \(140n\) to the left side:
\[ 180n - 140n = 360 \]
This simplifies to:
\[ 40n = 360 \]

### Step 7: Solve for \(n\).
Dividing both sides by 40:
\[ n = \frac{360}{40} = 9 \]

### Conclusion:
The polygon has \(9\) sides.