What is the maximum exterior angle of possible for a regular polygon if the measure of a one external angle of a regular polygon is 72 degree find the number of sides of the polygon

The formula to find the measure of one exterior angle of a regular polygon is:

\[
\text{Exterior Angle} = \frac{360^\circ}{n}
\]

where \(n\) is the number of sides of the polygon.

Given that the exterior angle is 72°, we can set up the equation:

\[
72^\circ = \frac{360^\circ}{n}
\]

To solve for \(n\), multiply both sides of the equation by \(n\) and divide both sides by 72°:

\[
n = \frac{360^\circ}{72^\circ} = 5
\]

Thus, the polygon has 5 sides, meaning it is a regular pentagon.

### Summary:
The polygon with an exterior angle of 72° has 5 sides.

Would you like more details, or do you have any other questions? Here are 5 related questions you can explore:

1. What is the sum of the interior angles of a regular pentagon?
2. How do you find the interior angle of a regular polygon?
3. What is the relationship between exterior and interior angles in polygons?
4. What would the exterior angle be for a regular hexagon?
5. Can a polygon have an exterior angle greater than 90°?

**Tip:** The sum of all exterior angles of any polygon always equals 360°, no matter the number of sides.

What is the maximum exterior angle possible for a regular polygon if the measure of one external angle of a regular polygon is 72 degrees? Find the number of sides of the polygon.

Discover how to find the number of sides in a regular polygon with an exterior angle of 72 degrees. This step-by-step solution explores the relationship between exterior angles and the number of sides in polygons, ideal for middle school students in Grades 6-8.

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