If an exterior angle of a regular polygon measures 45°, how many sides does the polygon have?

1. Break Down the Problem

To find the number of sides in a regular polygon given that an exterior angle measures $45^\circ$, we need to use the relationship between the measure of an exterior angle and the number of sides of the polygon.

2. Relevant Concepts

The formula to find the number of sides $n$ of a regular polygon using the measure of an exterior angle $E$ is given by: $n = \frac{360^\circ}{E}$ where $E$ is the measure of the exterior angle.

3. Analysis and Detail

In this case, $E = 45^\circ$. We can substitute this value into the formula: $n = \frac{360^\circ}{45^\circ}$

4. Verify and Summarize

Now, we will perform the calculation: $n = \frac{360}{45} = 8$

Final Answer

The polygon has $8$ sides.