No they dont because a hexagon does not have a right angle
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Not for every parallelogram. Only for a rhombus (diamond) or square will the diagonals bisect the opposite angles they connect, and diagonals are perpendicular. In rectangles, the diagonals do not bisect the angles and are notperpendicular, but they do bisect each other.
Every pair of supplementary angles includes one obtuse angle?
Every hexagon has.
Draw lines from every other angle that meet in the center.
Those acute angles all the central angles are acute.