What is the measure of an exterior angle in a regular polygon with 13 sides?Write your answer as an integer or as a decimal rounded to the nearest tenth.

1. Break Down the Problem

To find the measure of an exterior angle in a regular polygon, we need to determine how many sides the polygon has and then apply the formula for the exterior angle.

2. Relevant Concepts

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

3. Analysis and Detail

Here, $n = 13$ since the polygon has 13 sides. Now we can substitute the value of $n$ into the formula:

$E = \frac{360^\circ}{13}$

4. Verify and Summarize

Now, we perform the calculation:

$E = \frac{360}{13} \approx 27.692307692307693$

Rounding this to the nearest tenth gives us:

$E \approx 27.7$

Final Answer

The measure of an exterior angle in a regular polygon with 13 sides is approximately $27.7^\circ$.