To determine the minimum number of degrees that a star could be rotated so that it appears identical to its starting position, we need to consider the rotational symmetry of the star.
Assuming we are dealing with a typical star shape, such as a five-pointed star, we analyze its rotational properties. A five-pointed star can be rotated in increments that allow it to align with its original shape.
- Determine the Number of Points: A five-pointed star has 5 symmetrical points.
- Calculate the Rotation Angle: The total degrees in a full rotation is 360 degrees. Therefore, we can find the angle corresponding to one position that makes the star look the same by dividing the total degrees by the number of points:
\[ \text{Angle of rotation} = \frac{360^\circ}{5} = 72^\circ \]
This means that rotating the star by 72 degrees results in a configuration that appears the same as the original configuration.
For any star shape, while the specific number of degrees may vary based on the number of points, the formula to find the minimum angle for any n-pointed star is:
\[ \frac{360^\circ}{n} \]
Given that we have a star with 5 points, we calculated this as 72 degrees. If the star had a different number of points, the formula would still apply.
Thus, the minimum number of degrees that a star can be rotated so that it looks exactly the same is
\[ \boxed{72} \]