The problem asks to determine the minimum rotation (in degrees) that will carry a regular octagon onto itself. We need to find the smallest angle of rotation such that the octagon's sides and vertices match up.

1. Problem Description

The problem asks to determine the minimum rotation (in degrees) that will carry a regular octagon onto itself. We need to find the smallest angle of rotation such that the octagon's sides and vertices match up.

2. Solution Steps

A regular polygon with $n$ sides has rotational symmetry. The minimum angle of rotation required to map the polygon onto itself is given by:

$\frac{360}{n}$

In this case, the polygon is a regular octagon, so $n = 8$. Therefore, the minimum angle of rotation is:

$\frac{360}{8}$

$\frac{360}{8} = 45$

The minimum rotation is $45$ degrees. Since the problem asks to round the answer to two decimal places if necessary, we can write $45$ as $45.00$.

3. Final Answer

$45.00$