Is it possible to have a regular polygon each of whose exterior angles is `50^(@)` ?

Answer

To determine if it is possible to have a regular polygon where each exterior angle is \(50^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the exterior angle of a polygon**:
The exterior angle of a regular polygon can be calculated using the formula:
\[ \text{Exterior Angle} = \frac{360^\circ}{n} \]
where \(n\) is the number of sides of the polygon.

2. **Set up the equation with the given exterior angle**:
We know that the exterior angle is \(50^\circ\). Therefore, we can set up the equation:
\[ 50^\circ = \frac{360^\circ}{n} \]

3. **Rearrange the equation to solve for \(n\)**:
To find \(n\), we can rearrange the equation:
\[ n = \frac{360^\circ}{50^\circ} \]

4. **Calculate the value of \(n\)**:
Now, we perform the division:
\[ n = \frac{360}{50} = 7.2 \]

5. **Determine if \(n\) is an integer**:
Since \(n = 7.2\) is not an integer, it indicates that it is not possible to have a regular polygon with each exterior angle measuring \(50^\circ\).

6. **Conclusion**:
Therefore, it is not possible to have a regular polygon where each exterior angle is \(50^\circ\).