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Polygons

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by kartikshah » Fri Jul 27, 2012 5:30 am
As the number of sides of the polygon increases, what happens to the measures of each exterior angle of a regular polygon?

Source: www.gmatscore.com

As n approaches infinity, interior angles will become 180 degrees and consequently exterior angles will come close to zero. BUT my question is how is such a polygon possible? It would then become a line, isn't it?
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by Brent@GMATPrepNow » Fri Jul 27, 2012 12:28 pm
kartikshah wrote:As the number of sides of the polygon increases, what happens to the measures of each exterior angle of a regular polygon?

Source: www.gmatscore.com

As n approaches infinity, interior angles will become 180 degrees and consequently exterior angles will come close to zero. BUT my question is how is such a polygon possible? It would then become a line, isn't it?
We can see a trend towards 180-degree interior angles by examining a few examples.

3-sided regular polygon (equilateral triangle): Interior angles = 60 degrees
4-sided regular polygon (square): Interior angles = 90 degrees
5-sided regular polygon: Interior angles = 108 degrees

As the number of sides gets larger, the interior angles approach 180 degrees.

That said, I'm not sure how we'd use this theorem on a GMAT question.

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Brent
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by tutorphd » Fri Jul 27, 2012 7:48 pm
As the number of sides of a regular polygon increases, the poligon becomes closer and closer to a circle.

What's important to know on GMAT, is that the sum of the exterior angles of any convex polygon, not only regular one, is 360 degrees. That represents a rotation in direction by a full revolution, starting at a vertex, rotating each side with respect to the previous side by the external angle there, and coming back at the same vertex at the end.
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