SOLUTION: The measures of the angles of a regular polygon are whole numbers. What is the greatest number of sides that the polygon can have? Explain. THank you!

Question 951156: The measures of the angles of a regular polygon are whole numbers. What is the greatest number of sides that the polygon can have? Explain.
THank you!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The measures of the angles of a regular polygon are whole numbers. What is the greatest number of sides that the polygon can have? Explain.
----------------
360 sides.
That makes the exterior angles 1 deg, and the interior 179 degs.
Any more than 360 sides will make the angles non-integers.
=====================
Unless you consider a circle to be a polygon with an infinite # of sides.
Then each interior angle = 180 degs.
RELATED QUESTIONS
find the number of sides of a regular polygon in which each exterior angles measures... (answered by vleith)

What is the number of sides of a regular polygon if one angle measures... (answered by MathLover1,Gogonati)

What is the number of sides of a regular polygon if one angle measures 168... (answered by stanbon)

what is the number of sides of a regular polygon whose interior angles measure 135... (answered by Alan3354)

what is the sum of the measures of interior angles of a regular polygon with 38 sides. (answered by Alan3354)

If the exterior angles of a regular polygon are double the interior angles, what is the... (answered by Alan3354)

The following polygons are given. All of the polygons are regular polygons. Polygon... (answered by Edwin McCravy,solver91311)

one exterior angle of a regular polygon measures 10 degrees what is the measure of each... (answered by Alan3354)

A regular polygon has each of its angles 160degree.what is the number of sides of its... (answered by Alan3354,MathTherapy)