SOLUTION: in a regular polygon, each exterior angle is 140 degrees less than each interior angle. How many sides has the polygon?

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Question 855465: in a regular polygon, each exterior angle is 140 degrees less than each interior angle. How many sides has the polygon?
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
ext angles = 20 degs
360/20 = 18 sides

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
An exterior angle is the angle you turn at each vertex as you go around the polygon:
The sum of the measures of all exteror angles is 360%5Eo .
An exterior angle is supplementary to the interior angle,
so if x= measure of each exterior angle in degrees,
x%2B140= measure of each interior angle in degrees,
and x%2B%28x%2B140%29=180 .

Solving for x :
x%2B%28x%2B140%29=180
%28x%2Bx%29%2B140=180
2x%2B140=180
2x=180-140
2x=40
x=40%2F2
x=20

If it is a regular polygon with n sides, it has n exterior angles,
each measuring 20%5Eo , and the sum of their measures (in degrees) is
20n=360 --> n=360%2F2 --> highlight%28n=18%29
The polygon has highlight%2818%29 sides.