First draw a circle. Keeping the compass at the same angle; from any point on the circle's edge, draw another arc that intersects the circle's edge and (should) go through the centre as well. Repeat these arcs until you get back to the start. Using a ruler, connect the six intersect points on the edge of the circle and erase the construction lines.
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Yes. Bees are extremely good at tessellating regular hexagons in a honeycomb.
120 you can find the angle of any regular polygon by using this formula...n is the number of sides ((n*180)-360)/n