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Below are some examples of pictures made by taking a regular polygon and rotating it by a fixed angle about one of its vertices.
Can you work out the polygon used and the angle of rotation in each picture?
How many other angles in each picture can you calculate?
Try drawing some pictures of your own in this way. You may wish to use GeoGebra. You could challenge a friend to work out which polygon you used and the size of all the angles.
You may find it useful to print out the figure.
If you enjoyed this problem, you may be interested in Attractive Rotations and in the other problems in our Angles and Polygons Feature.
How can you make an angle of 60 degrees by folding a sheet of paper twice?
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.
Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.