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Let A_1 A_2 A_3 ... A_{10} be a regular polygon.  A rotation centered at A_1 with an angle of a takes A_2 to A_{10}.  Given that a < 180 degrees, find a, in degrees.

 Jan 2, 2022
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Visualizing, you can see that for the angle to the left of the top angle to be to the right of the top angle, we have to rotate the polygon 144 degrees around A_1.  A way to think about it is to have the side to the left of A_1 be moved to the right of A_1.  In order to do this, we must rotate 144 degrees, shown in the diagram.  

 

Thus, the answer is 144 degrees.

 

 Jan 2, 2022

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