Measuring implies using a measuring device of some kind. If you mean to construct a hexagon without a protractor or ruler, that's different. Constructions in geometry require only a compass and a straightedge (a ruler, but you ignore the numbers).
A hexagon can be made of 6 equilateral triangles; choose any length for the side and construct them connected together, using only the compass to set the length and the straightedge to draw straight lines between points.
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a ruler measures the distance and a protractor measures the angles
A ruler. Add a line to make the angle into a triangle, measure the sides and use trigonometry.
A "protractor" is a device that can be used to draw angles of a specified size, or measure the size of unknown angles, in the same way that a "ruler" is used to do the same thing with lines.
A protractor is used to measure angles.