A hexagon has no right angles.
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A regular 6 sided hexagon has no right angles but it's quite possible for an irregular hexagon to have right angles.
It is a hexagon with two right angles: there is no special name for such a shape.
If 1 or 2 of the obtuse angles are 'bent into' the hexagon then you can do it.A hexagon has 720° sum of interior angles. If you have 2 right angles, then that's 180°, leaving 540° to be distributed over four angles. If the two acute angles are 89°, then that leaves 362° to be divided between two angles, so at least one of these two angles will need to be greater than 180°. Below is my text graphics attempt of one possibility (ignore the 'dot'). Note that both of the obtuse angles are greater than 180°:|\_/||__.|Look at the related link to play with different angle possibilities for polygons.
A regular hexagon has six equal internal angles of 120 degrees. None of them are right-angles !
Irregular hexagon has 2 right angles all other sides are congruent. How large is each one?