A regular hexagon (all sides and angles congruent) has no right angles, although it's possible that an irregular hexagon could. All hexagons have six sides and six angles. The angles must add up to 720°. So it would be possible to have as many as 5 angles equal 90° (5 x 90° = 450°), and one angle equal 270° (450° + 270° = 720°).
Take a rectangle then cut a rectangular notch at one of the corners. You now have 6 sides and 6 angles. Five of the angles are right angles (90°). The sixth angle looks like a right angle, but it is 'cut in' (the polygon is concave, now): the measure of this angle is 270°.
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A hexagon has no right angles.
A regular hexagon has six equal internal angles of 120 degrees. None of them are right-angles !
A regular 6 sided hexagon has no right angles but it's quite possible for an irregular hexagon to have right angles.
None. A hexagon has eight angles all of which are 45 degrees. A right angle has 90 degrees.
It is a hexagon with two right angles: there is no special name for such a shape.