Okay, so I need to figure out the minimum number of degrees a regular pentagon must be rotated counterclockwise about its center until it coincides with its original position. Hmm, let's start by recalling some basic concepts about regular polygons and their rotational symmetry.

First, a regular pentagon has all sides equal and all interior angles equal. When you rotate a regular polygon about its center, the smallest angle you can rotate it so that it looks exactly the same as it did before the rotation is called the order of rotation. The number of positions it can occupy before returning to its original position is equal to the number of sides. For a regular polygon with 'n' sides, the smallest rotation angle that maps the polygon onto itself is 360 degrees divided by 'n'. 

Wait, so for a regular pentagon, which has 5 sides, the smallest rotation angle should be 360 divided by 5. Let me check that. 360 divided by 5 is 72 degrees. So does that mean if you rotate the pentagon 72 degrees counterclockwise, it will look the same as before? Let me visualize this. If you rotate a regular pentagon by 72 degrees, each vertex moves to the position of the next vertex. Since there are five vertices, after five such rotations, each vertex would have returned to its original position. That makes sense. 

But let me make sure I'm not missing anything here. The key point is that the rotation has to be such that every vertex and every side maps exactly onto their original positions. Since a regular pentagon has rotational symmetry of order 5, the smallest angle of rotation that maps it onto itself must be 360/5 = 72 degrees. 

Let me think if there's a different way this could be approached. Maybe by considering the central angles of the pentagon. Each central angle (the angle at the center between two adjacent vertices) is equal to 360 divided by the number of sides, so again 72 degrees. So rotating by that central angle would align the vertices with their original positions. 

Another way to verify this is to think about the dihedral angles of the pentagon. The dihedral group for a regular pentagon includes rotations by multiples of 72 degrees. So the minimal non-zero rotation that maps the pentagon onto itself is indeed 72 degrees. 

I don't think there's a smaller angle than 72 degrees that would satisfy the condition. If I tried rotating by, say, 36 degrees, which is a divisor of 72, would that work? Let's see. If you rotate 36 degrees, each vertex would not align with the next vertex because 36 doesn't divide evenly into 360 in a way that cycles through all five vertices. Specifically, 360 divided by 36 is 10, so after 10 such rotations, you'd get back to the original position, but since there are only 5 vertices, each rotation of 36 degrees would cycle through two positions (because 36 is 360/10, so every 36 degrees moves each vertex by 2 positions). Therefore, after 5 rotations of 36 degrees, each vertex would have moved 10 positions, which is equivalent to 0 mod 5, so they would return to their original places. Wait, but that's 5 rotations of 36 degrees each, totaling 180 degrees. But that seems contradictory because 72 degrees is smaller than 180. 

Wait, maybe I'm confusing something here. Let me clarify. The order of rotational symmetry is the number of distinct orientations the polygon can take that look the same. For a regular pentagon, that's 5. Therefore, the angle between each orientation is 360/5 = 72 degrees. So any rotation that is a multiple of 72 degrees will map the pentagon onto itself. So rotating by 72, 144, 216, 288, or 360 degrees (which is the same as 0 degrees) will result in the pentagon coinciding with its original position. 

Therefore, the minimal positive rotation angle required is 72 degrees. 

I think that's solid. To recap: For regular polygons, the minimal rotation angle to coincide with original position is 360/n degrees, where n is the number of sides. For a pentagon, n=5, so 72 degrees. 

I don't see any flaws in this reasoning. It's consistent with the properties of rotational symmetry in regular polygons. So the answer should be 72 degrees.
Therefore, the minimum number of degrees the regular pentagon must be rotated counterclockwise about its center until it coincides with its original position is $\boxed{72}$ degrees.
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