A regular hexagon, of course, has no right angles, but irregular, convex hexagons can have one, two, or three right angles.

With one right angle, there is only one basic configuration, but, with two right angles, there are three: the right angles may be consecutive, have one non-right angle between them, or be opposite angles.

There are also three possible configurations with three right angles: the three angles can be consecutive, or two can be consecutive with one non-right angle separating the other right angle from the consecutive pair, or every other angle can be a right angle.

Four right angles cannot exist in a convex hexagon, nor can five, nor, of course, six. Four right interior angles are possible, however, for non-convex hexagons, and, again, there are three possible configurations. In the first, the four right angles are consecutive. In the second, three are consecutive, then a non-right angle separates the fourth right angle from the other three. In the third, there are two pairs of consecutive right angles, with single non-right angles separating the pairs on opposite sides of the hexagon.

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