1. The problem asks which of the given angles could be the size of an exterior angle of a regular polygon. 2. The formula for the exterior angle $E$ of a regular polygon with $n$ sides is: $$E = \frac{360}{n}$$ where $n$ must be a positive integer greater than 2. 3. To determine if an angle can be an exterior angle, check if $\frac{360}{E}$ is a positive integer. 4. Check each angle: - For $15^\circ$: $\frac{360}{15} = 24$ (integer, valid) - For $32^\circ$: $\frac{360}{32} = 11.25$ (not integer, invalid) - For $90^\circ$: $\frac{360}{90} = 4$ (integer, valid) - For $165^\circ$: $\frac{360}{165} = \frac{360}{165} = \frac{24}{11}$ (not integer, invalid) - For $200^\circ$: $\frac{360}{200} = 1.8$ (not integer, invalid) 5. Therefore, the possible exterior angles are $15^\circ$ and $90^\circ$. Final answer: $15^\circ$ and $90^\circ$