Each of the five marked angles measures $360/5=72$ degrees, so $\boxed{72}$ degrees is the minimum angle through which the pentagon may be rotated so that it coincides with its original position.

[asy]
size(150);
defaultpen(linewidth(0.7));
int i;
for(i=0;i<=4;++i)

{
draw(origin--dir(18+72*i)--dir(18+72*(i+1)));
draw(anglemark(dir(18+72*i),origin,dir(18+72*(i+1)),3+fmod(i,3)));
}
[/asy]
Question:
A regular pentagon is rotated counterclockwise about its center. What is the minimum number of degrees it must be rotated until it coincides with its original position?
Answer:
Let's think step by step.

user
72
A regular pentagon is rotated counterclockwise about its center. What is the minimum number of degrees it must be rotated until it coincides with its original position?
test