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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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    @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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    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