It depends on what the angles are. If any of the angles have measurements greater than 180 degrees, it is concave. If all angles are less than 180 degrees, then it is concave. For example, a regular hexagon has six 120 degree angles, so it is convex. If there was a hexagon with five 90 degree angles and one 270 degree angle, it would be concave.
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Any hexagon has six sides.
It can be but need not be.
A regular hexagon has zero right angles. An irregular convex hexagon could have 0-3.
Some concave hexagons can. For an extremely crude figure, but the best that this browser will allow, see below (the full stops are only for positioning the diagonals):____________\.................\..\.................\../................//___________/
No. A hexagon is a 6-sided figure. A parallelogram is a specific kind of 4-sided figure.