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What is exactly meant by "angle subtended by all sides of a polygon at its center" ? I encountered these while solving this problem:

How can we determine the number of sides of a polygon,given the angles subtended by all the side at its center are equal to $72 ^\circ$?

Could somebody please explain (with a figure) what is meant to calculate in this question?

EDIT: I tried to Google some help, which took me to this page.I think this is what meant in this question.If so why all sides is mention in this question? and why it is supposed that the polygon will have equal sides?

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Here's a rough diagram showing the center of the polygon and some sides and indicating the angle that is subtended by a side.

diagram

You are given that the measure of all such angles in a particular polygon is 72° and asked to determine the number of sides in the polygon.

edit: As to why "all sides" is used in the problem, I'd guess it's a translation/language issue and that "each side" is a more appropriate description of what was intended.

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    I really appreciate your efforts but I guess i have edited the question while you are writing the answer,so I guess it's the same idea explained in that link.But I am not sure why `all sides meant` and why it is supposed that all sides will have equal lengths ?!2011-01-05
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    @Debanjan: After seeing your edit, I added a note at the end of my answer regarding the "all sides" language--I think it probably should have said "each side." I don't see where you're getting the equal lengths part, though.2011-01-05
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    Thanks a lot, I am not sure if I am correct or not but what about this polygon: http://tinyurl.com/2whfcwh or we cannot have a center for this ?2011-01-05
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    @Debanjan: I think, for non-regular polygons, "center" is probably not well-defined. (There are [thousands of known centers for triangles](http://faculty.evansville.edu/ck6/encyclopedia/).) "centroid" (center of mass assuming uniform distribution of mass across the area of the polygon) might be a reasonable choice for a "center," at least for convex polygons.2011-01-05
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    Hm so we have to assume regular polygons only. Thanks Issac :)2011-01-05
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    @Debanjan: I don't think it's necessary to assume that in this problem. I think it's sufficient to assume that "center" refers to some point in the interior of the polygon and that the polygon is convex.2011-01-05
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    @Jasper: Thanks. Having good tools helps a lot (this diagram came from Geometer's Sketchpad 5; others have used Mathematica 7 and Adobe Illustrator CS3 and CS5). As to thousands of triangle centers, 3597 as of 09/18/2010 16:01:13, according to the link in my earlier comment, so pretty literal.2011-01-05
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If there are 360 degrees in a circle...

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    It seems like I haven't understood the problem actually from your answer it seems like you are hinting for $\frac{360}{72}$ but the 3D/2D diagram for this problem is not clear in my head,may be due the words I am confusing.2011-01-05
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    That was exactly my point. I didn't seen anything about 3D in the question. The reason the page you link to calls for equal sides is so you can divide by n. If the sides are not equal (and even if they are equal if the angles are not) they may not all subtend the same angle.2011-01-05