SOLUTION: the measure of one interior angle of a regular polygon is 6 greater than twice the measure of an exterior angle at the same vertex. How many sides does the polygon have?

Question 778882: the measure of one interior angle of a regular polygon is 6 greater than twice the measure of an exterior angle at the same vertex. How many sides does the polygon have?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the measure of one interior angle of a regular polygon is 6 greater than twice the measure of an exterior angle at the same vertex. How many sides does the polygon have?
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Each int/ext pair of angles is supplementary.
Equation:
int + ext = 180
int = 2*ext + 6
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Substitute for int and solve for ext:
2ext + 6 + ext = 180
3ext = 174
ext = 58 degrees
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The sum of all of the exterior angle is 360 degrees
# of sides = # of ext angles = 360/58 = 6.2069
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Note: Part of the directions for the problem must be incorrect.
The # of sides should be a whole number.
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Cheers,
Stan H.

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