SOLUTION: is it possible to make a regular polygon where each interior angle is exactly 9 times as large as the matching exterior angle?

Question 940570: is it possible to make a regular polygon where each interior angle is exactly 9 times as large as the matching exterior angle?
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
is it possible to make a regular polygon where each interior angle is exactly 9 times as large as the matching exterior angle?
-------------
Yes.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The exterior angle and the interior angle are supplementary,
meaning that they add up to .
Let be the measure of the exterior angle in degrees.
Then, is the measure of the interior angle in degrees, and
"each interior angle is exactly 9 times as large as the matching exterior angle" translates as
<---><---><---><---> .
The exterior angle is the angle you turn around the corner/vertex, as you go around the polygon. Naturally, once you went all the way around, you have turned , so the sum of the measures of all exterior angles is .
All the exterior angles in a regular polygon have the same measure,
so if each exterior angle measures ,
the sum of the exterior angles in the polygon is
<---><---> .
It is possible to make a polygon with 20 sides angles, so the answer is .
If we had found a result for that was not a whole number, or was a whole number less than 3, the answer would have been no.
RELATED QUESTIONS
the interior angle of a regular polygon is 8 times as large as the exterior angle.... (answered by MathTherapy)
A regular polygon's interior angle is 8 times as large as its exterior... (answered by jim_thompson5910,ikleyn,MathTherapy)
Is it possible to have a regular polygon where each interior angle is equal to 145? If... (answered by Alan3354)
What is the exterior angle of a regular polygon in which the interior angle is three... (answered by ikleyn)
as the number of sides of a regular polygon increases, What happens to the measure of... (answered by solver91311)
Each interior angle of a regular polygon is 20 more than 3 times the measure of each... (answered by stanbon)
THE SIZE OF EACH INTERIOR ANGLE OF A REGULAR POLYGON IS 11 TIMES THE SIZE OF EACH... (answered by stanbon)
Each interior angle of a regular polygon is thrice each exterior angle. Find the number... (answered by Edwin McCravy)
{{{The measure of each interior angle of a regular polygon is three times the measure of... (answered by Alan3354)