How to get [consistent] central angles of a regular polygon?

shaco shared this question 8 years ago

I created a regular10-gon of fixed side length.

You'd think that the central angle between any of the 10 sides would be 360°/10 = 36°.

But, GeoGebra gives me the following 10, mostly different, central angles when they should all be the same!

36.04°, 36.03°, 36°, 35.97°, 35.96°, 35.96°, 35.97°, 36°, 36.03°, 36.04°.

360°/10 = 36° is the expected, easy, and exact value, so I don't want to tell a youngster that GeoGebra is just having problems with round-off errors.

I know I can force the rounding to be 0 or 1 decimals to force apparent agreement among the 10 central angles, but how could a young student discover that they are really, mathematically, all the same?

Below is another attempt -- and the angles were different again!

Comments (4)


Using regular polygon tool and

try: K=Centroid[poly1]

This may assist,



Your Point K is not correct - you've placed it "by eye". If you use the Intersect Tool, it will be much more accurate.



Yes, murkle is right. If you just change the definition of K from Point[l] to MidPoint[l] it will work properly.


Thank you so much acron, murkle, and M_OLoughlin!

What I learned is NOT to use "Point On Object" to place a point at the intersection of more than two objects. (Even though it's worked in the past when I've intersected two line segments, for example.)

Instead, I will either use "Intersect Two Objects," or redefine the intersection as you suggested.

Thanks again!

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