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3. Is it possible to have a regular polygon with each exterior angle measuring [tex]58^\circ[/tex]? Why or why not? Can it be an interior angle of a regular polygon?

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Final answer:

It is not possible to have a regular polygon with each exterior angle measuring 580 degrees; the internal angle cannot be negative.


Explanation:

No, it is not possible to have a regular polygon with each exterior angle measuring 580 degrees. In a regular polygon, all exterior angles are equal, so if one exterior angle measures 580 degrees, all the other exterior angles would also need to measure 580 degrees, leading to a total sum greater than 360 degrees (the sum of exterior angles in any polygon).

On the other hand, interior angles of a regular polygon are related to exterior angles by the formula: interior angle + exterior angle = 180 degrees. Therefore, if the exterior angle is 580 degrees, the interior angle would be 180 - 580 = -400 degrees, which is not geometrically feasible.


Learn more about Polygon angles here:

https://brainly.com/question/42413256


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