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

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) (Show Source): You can put this solution on YOUR website!
ext angles = 20 degs
360/20 = 18 sides
Answer by KMST(5328) (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 .
An exterior angle is supplementary to the interior angle,
so if = measure of each exterior angle in degrees,
= measure of each interior angle in degrees,
and .

Solving for :

If it is a regular polygon with sides, it has exterior angles,
each measuring , and the sum of their measures (in degrees) is
--> -->
The polygon has sides.
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