SOLUTION: True or False is it possible for each exterior angle of a regular polygon to be 8 degrees?

Algebra.Com
Question 892200: True or False
is it possible for each exterior angle of a regular polygon to be 8 degrees?
Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Yes.  The sum of the exterior angles of any convex polygon is 360°.  Since this
is a regular polygon the polygon has all its exterior angles the same, so each
one would be , so we have the equation:



Multiply both sides by n



Divide both sides by 8°





So it has 45 sides.  It looks like this figure below, without the
"spokes". Notice that the green lines are the extensions of two 
adjacent sides and the angle between those two green lines is an 
exterior angle of 8°.



Edwin
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
360/8 = 45
that would be a 45 sided figure.
the interior angle of each of the vertices would be 180 - 8 = 172 degrees.
the formula for the interior angle of a 45 sided figure would be [(45-2) * 180] divided by 45 which is equal to [43 * 180 / 45] which is equal to 43 * 4 which is equal to 172 degrees.
yes it is possible.
the regular figure would have 45 sides.
each internal angle at each vertex would be equal to 172 degrees.
each external angle at each vertex would be equal to 8 degrees.


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