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It varies. If it has reflex angles, then it varies, depending on the number of reflex angles and their location in relation to each other. Otherwise (if it has no reflex angles) then it has 4 diagonals.
A hexagon with two reflex angles opposite one another will have two diagonals that lie entirely outside the hexagon and one that is partly outside.
No - only one of the diagonals bisects the angles of the shape.
In rhombuses and squares the diagonals bisect opposite angles.
No, the diagonals of a parallelogram do not necessarily bisect the angles. The diagonals of a parallelogram divide it into four congruent triangles, but they do not necessarily bisect the angles of those triangles.