It went viral after students were stumped.
This question went viral after it stumped grade 12 students in Australia. There are two ways to think about the problem.
1. x is double an exterior angle
If you think about the exterior angles of the coin (those in blue shown below), they form a total of 360 degrees, as is true for all convex polygons (triangles, squares, hexagons, etc.). In this case, the coin is a dodecagon and thus has 12 sides, 12 corners and 12 equal angles. We can figure out that a single angle is 360/12=30 degrees, so x = 60 degrees.
2. Three dodecagons will leave an equilateral triangle
When dodecagons tile a flat surface, they leave equilateral triangles between them. If we look at the image below, we can see that the angle x is one of the three interior angles of the green equilateral triangle and therefore must be 60 degrees.
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