Final answer:
The minimum number of degrees a regular pentagon must be rotated about its center to look the same is 72 degrees, due to its rotational symmetry.
Step-by-step explanation:
The student's question relates to a regular pentagon and its rotational symmetry.
A regular pentagon has five equal sides and angles, and it exhibits rotational symmetry.
Rotational symmetry of an object means that the object looks the same after a certain amount of rotation about its center.
To determine the minimum number of degrees a regular pentagon must be rotated about its center to look the same, you would divide 360 degrees by the number of sides of the pentagon.
Since a pentagon has 5 sides, you would rotate it 360°/5 = 72°.
Therefore, the regular pentagon must be rotated by a minimum of 72 degrees about its center for it to appear as it did before the rotation.