If each interior angle of regular polygon is `144^(@)` then what is the number of sides in the polygon

Options

A. 10
B. 20
C. 24
D. 36

Answer

To find the number of sides in a regular polygon where each interior angle is \(144^\circ\), we can use the formula for the interior angle of a regular polygon:

\[ \text{Interior Angle} = \frac{(n - 2) \times 180}{n} \]

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

### Step 1: Set up the equation
Given that each interior angle is \(144^\circ\), we can set up the equation:

\[ 144 = \frac{(n - 2) \times 180}{n} \]

### Step 2: Multiply both sides by \(n\)
To eliminate the fraction, we multiply both sides of the equation by \(n\):

\[ 144n = (n - 2) \times 180 \]

### Step 3: Expand the right side
Now, we expand the right side:

\[ 144n = 180n - 360 \]

### Step 4: Rearrange the equation
Next, we rearrange the equation to isolate \(n\):

\[ 144n - 180n = -360 \]

This simplifies to:

\[ -36n = -360 \]

### Step 5: Solve for \(n\)
Now, we divide both sides by \(-36\):

\[ n = \frac{-360}{-36} = 10 \]

### Conclusion
Thus, the number of sides in the polygon is \(n = 10\).