If each interior angle of a regular polygon is `144^@`, find the number of sides in it.

Options

A. No. of sides =`9`
B. No. of sides =`10`
C. No. of sides =`11`
D. No. of sides =`13`

Answer

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

### Step-by-Step Solution:

1. **Understand the formula for the interior angle of a regular polygon**:
The formula for the measure of each interior angle of a regular polygon with \(n\) sides is given by:
\[ \text{Interior Angle} = \frac{(n-2) \times 180}{n} \]
where \(n\) is the number of sides.

2. **Set up the equation**:
Since we know that each interior angle is \(144^\circ\), we can set up the equation:
\[ 144 = \frac{(n-2) \times 180}{n} \]

3. **Cross-multiply to eliminate the fraction**:
To eliminate the fraction, we cross-multiply:
\[ 144n = (n-2) \times 180 \]

4. **Expand the right side**:
Expanding the right side gives:
\[ 144n = 180n - 360 \]

5. **Rearrange the equation**:
Now, we rearrange the equation to isolate \(n\):
\[ 180n - 144n = 360 \]
Simplifying this gives:
\[ 36n = 360 \]

6. **Solve for \(n\)**:
Finally, divide both sides by \(36\) to find \(n\):
\[ n = \frac{360}{36} = 10 \]

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

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