For a regular polygon of n sides we have
Sum of all exterior angles………

Options

A. `180^@`
B. `270^@`
C. `360^@`
D. `540^@`

Answer

To find the sum of all exterior angles of a regular polygon with \( n \) sides, follow these steps:

### Step-by-Step Solution:

1. **Understanding Exterior Angles**:
- Each exterior angle of a regular polygon is formed by extending one side of the polygon at each vertex. For a regular polygon, all exterior angles are equal.

2. **Formula for Each Exterior Angle**:
- The measure of each 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.

3. **Calculating the Sum of Exterior Angles**:
- Since there are \( n \) exterior angles in a polygon, the sum of all exterior angles can be calculated as:
\[ \text{Sum of Exterior Angles} = n \times \left(\frac{360^\circ}{n}\right) \]

4. **Simplifying the Expression**:
- When you simplify the expression:
\[ \text{Sum of Exterior Angles} = \frac{360^\circ \times n}{n} = 360^\circ \]

5. **Conclusion**:
- Therefore, the sum of all exterior angles of a regular polygon with \( n \) sides is always:
\[ \text{Sum of Exterior Angles} = 360^\circ \]

### Final Answer:
The sum of all exterior angles of a regular polygon with \( n \) sides is \( 360^\circ \).

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