Each exterior angle of regular polyon of n side is equal to

Options

A. `4n xx 90^@`
B. `(360^@)/(n)`
C. `(2n-4) xx 90^@`
D. `4 xx 90^@`

Answer

To find the measure of each exterior angle of a regular polygon with \( n \) sides, follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Exterior Angles**:
Each exterior angle of a 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 Exterior Angles**:
For a regular polygon (where all sides and angles are equal), the measure of each exterior angle can be calculated using the formula:
\[ \text{Sum of exterior angles} = \text{Number of sides} \times \text{Measure of each exterior angle} \]
Since the sum of the exterior angles is \( 360^\circ \), we can express this as:
\[ 360^\circ = n \times \text{Measure of each exterior angle} \]

3. **Isolate the Measure of Each Exterior Angle**:
To find the measure of each exterior angle, we rearrange the formula:
\[ \text{Measure of each exterior angle} = \frac{360^\circ}{n} \]

4. **Conclusion**:
Therefore, the measure of each exterior angle of a regular polygon with \( n \) sides is:
\[ \text{Measure of each exterior angle} = \frac{360^\circ}{n} \]

### Final Answer:
Each exterior angle of a regular polygon with \( n \) sides is equal to \( \frac{360^\circ}{n} \).

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