1. **State the problem:** We have a Ferris wheel with 8 evenly spaced gondolas arranged in a circle. We need to find the order of rotational symmetry and the smallest angle of rotation that maps the wheel onto itself. 2. **Formula and rules:** The order of rotational symmetry for an object with $n$ evenly spaced identical parts is $n$. The smallest angle of rotation that maps the object onto itself is given by: $$\text{Smallest angle} = \frac{360^\circ}{n}$$ 3. **Apply to the problem:** Here, $n=8$ gondolas. Order of rotational symmetry = $8$ Smallest angle of rotation: $$\frac{360^\circ}{8} = 45^\circ$$ 4. **Interpretation:** This means the Ferris wheel looks the same after rotating it by $45^\circ$, and there are 8 such rotations in a full $360^\circ$ turn. **Final answer:** - Order of rotational symmetry: $8$ - Smallest angle of rotation: $45^\circ$