What is the measure of an exterior angle of a regular polygon of 5 sides?

Options

A. 72
B. 60
C. 45
D. 40

Answer

To find the measure of an exterior angle of a regular polygon with 5 sides, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the property of exterior angles**: The sum of all exterior angles of any polygon is always 360 degrees.

2. **Determine the number of sides**: For a regular polygon with 5 sides, we denote the number of sides as \( n = 5 \).

3. **Calculate the measure of each exterior angle**: Since the polygon is regular, all exterior angles are equal. Therefore, the measure of each exterior angle can be calculated using the formula:
\[ \text{Measure of each exterior angle} = \frac{\text{Sum of exterior angles}}{n} = \frac{360^\circ}{n} \]

4. **Substitute the value of \( n \)**: Plugging in the value of \( n \):
\[ \text{Measure of each exterior angle} = \frac{360^\circ}{5} \]

5. **Perform the division**:
\[ \text{Measure of each exterior angle} = 72^\circ \]

6. **Conclusion**: The measure of an exterior angle of a regular polygon with 5 sides is \( 72^\circ \).

### Final Answer:
The measure of an exterior angle of a regular polygon with 5 sides is **72 degrees**.

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