Final answer:A regular hexagon will coincide with itself when rotated by angles of 60 degrees, or multiples of it like 120, 180, 240, 300, and 360 degrees, because these are the angles of rotational symmetry for a hexagon.Explanation:A regular hexagon has six sides of equal length and interior angles that are also equal. When a regular hexagon is rotated about its center, there are specific degree measures for which it will fit exactly onto itself, known as the angles of rotational symmetry. Since a full rotation measures 360 degrees and a hexagon has six sides, we can divide 360 degrees by the number of sides to find the smallest angle of rotation that will carry the regular hexagon onto itself.The calculation is 360 ÷ 6 = 60 degrees. Therefore, a regular hexagon will coincide with itself every 60-degree turn. Other angles that will carry the hexagon onto itself are multiples of 60 degrees: 120 degrees, 180 degrees, 240 degrees, 300 degrees, and 360 degrees (a full rotation)....

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