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.