Polygons

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kartikshah: Master | Next Rank: 500 Posts; Posts: 156; Joined: Sun Jul 15, 2012 12:03 pmFollowed by: 1 member; Location: New York, USA; Thanked: 34 times

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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Source: Beat The GMAT — Quantitative Reasoning | Fri Jul 27, 2012 5:30 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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tutorphd: Master | Next Rank: 500 Posts; Posts: 126; Joined: Sun Jun 24, 2012 10:11 amFollowed by: 7 members; Location: Chicago, IL; Thanked: 36 times

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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https://gmat.tutorchicago.org/

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