Any measure that you like. The measure can be uniquely determined only if it is a REGULAR hexagon.
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Providing that it is a regular hexagon then each exterior angle will measure 60 degrees
The 6 inside angles of a hexagon add up to 720 degrees
Exterior angle of a regular hexagon = 60 degrees
The hexagon has the larger exterior angle.
It depends on a few factors: if the angle is interior, if the angle is exterior, and if the hexagon is a regular hexagon or not. Each interior angle of a regular hexagon is 120o. Each exterior angle of a regular hexagon is 60o.