SOLUTION: a regular n-gon has a vertex angle that measure 140 degrees. based on the measure for this n-gon find: how many sides are there for this n-gon? what is the measure of an exterior

Question 493661: a regular n-gon has a vertex angle that measure 140 degrees. based on the measure for this n-gon find:
how many sides are there for this n-gon?
what is the measure of an exterior angle?
what is the measure of a central angle?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a regular n-gon has a vertex angle that measure 140 degrees. based on the measure for this n-gon find:
what is the measure of an exterior angle?
Ans: 180-140 = 40
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how many sides are there for this n-gon?
Since the sum of the exterior angles is 360,
# of ext. angles = 360/40 = 9
= # of sides
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what is the measure of a central angle?
Draw the picture and you will see
9 issosceles triangles.
The equal angles are (1/2)(140) = 70
Central angle = 180-2(70) = 40 degrees
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Cheers,
Stan H.
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