It's possible but usually not. But any two regularones are definitely always similar.
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The exterior angle of each hexagon can be any measure you like, including reflex angles. Two such hexagons can be joined together at any pair of angles that are smaller than 180 degrees. So the exterior angle formed can range from 0 to 360 degrees (excluding the two bounds).
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No. They're always in the same ratio.
Hexagons have six sides, not four. Any number of them can be of the same length.