Each exterior angle of a regular polygon of m sides is

Options

A. `(360/m)pi` degree
B. `(360/m)` degree
C. `(180/m)pi^2` degree
D. `(180/m)` degree

Answer

To find each exterior angle of a regular polygon with \( m \) sides, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Exterior Angles**:
Each exterior angle of a regular polygon is formed by extending one side of the polygon. The sum of all exterior angles of any polygon is always \( 360^\circ \).

2. **Formula for Each Exterior Angle**:
For a regular polygon, where all sides and angles are equal, the measure of each exterior angle can be calculated using the formula:
\[ \text{Each exterior angle} = \frac{360^\circ}{\text{Number of sides}} \]

3. **Substituting the Number of Sides**:
Since we are given that the polygon has \( m \) sides, we substitute \( m \) into the formula:
\[ \text{Each exterior angle} = \frac{360^\circ}{m} \]

4. **Final Result**:
Therefore, the measure of each exterior angle of a regular polygon with \( m \) sides is:
\[ \frac{360^\circ}{m} \]

### Conclusion:
The answer to the question is that each exterior angle of a regular polygon with \( m \) sides is \( \frac{360^\circ}{m} \).

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