1. The problem asks for the smallest angle of rotation that maps the image onto itself, given it has rotational symmetry. 2. The image is described as an 8-part pinwheel with alternating colors, meaning it has 8 identical segments arranged around a center. 3. The formula for the smallest angle of rotational symmetry is: $$\text{Smallest angle} = \frac{360^\circ}{n}$$ where $n$ is the number of identical segments. 4. Here, $n=8$, so: $$\text{Smallest angle} = \frac{360^\circ}{8}$$ 5. Simplify the fraction: $$\frac{360^\circ}{8} = 45^\circ$$ 6. Therefore, the smallest rotation angle for the image to look the same is $45^\circ$.