2)Through how many different positive angles less than 360 degrees is it possible to rotate a regular icosagon (20-gon) clockwise about its center such that its image coincides with the original icosagon?


3)A translation maps A to Aprime and B to Bprime. We know  AAprime = 3, AB = 4 and ABprime = 5.  Find BAprime.


5)A regular pentagon is rotated counterclockwise about its center by a nonzero angle. What is the minimum number of degrees it must be rotated until it coincides with its original position?



6)Jessica wants to add one more dot to the diagram below so that the four dots form the four vertices of a parallelogram. In how many possible locations can she put her dot?



8)A pentagon ABCDE is translated north by 40 units to pentagon A1B1C1D1E1. Pentagon A1B1C1D1E1 is then translated east by 50 units to pentagon A2B2C2D2E2. We know the perimeter of pentagon ABCDE is 30 units. Find CC2.


9)A and B are two points on a plane. A translation maps A to B and B to Bprime. Another translation maps B to A  and A to Aprime. We know AprimeBprime = 16. Find AB.


10)OPQRSTUVWX is a regular decagon (10-gon). A rotation of theta degrees about U maps X to R. Given theta < 180 degrees, find theta.



11)Let ABCD be a square of side length 1. Let P be a point on side CD such that angle DAP = 20 degrees. Let Q be a point on side BC such that angle BAQ = 25 degrees. Find the perimeter of triangle CPQ.


FiestyGeco  Apr 25, 2018

For your info, these are copyrighted problems from AoPS, and sharing these problems with others is a copyright infringement. 

Guest May 17, 2018

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