If a regular polygon has eight sides, what is the measure of one of its exterior angles?

To determine the measure of one exterior angle of a regular polygon, you can use the formula:

[

\text{Exterior Angle} = \frac{360^\circ}{n}

]

where ( n ) is the number of sides of the polygon. In this case, since we are dealing with an octagon, ( n ) is equal to 8.

Applying the formula:

[

\text{Exterior Angle} = \frac{360^\circ}{8} = 45^\circ

]

This calculation shows that each exterior angle of a regular octagon measures 45 degrees.

Given that the question asks for the measure of one exterior angle, the correct answer should not be identified as 135 degrees. That value does not fit the context for an exterior angle in a regular octagon.

Thus, while the answer provided in the initial response identifies an alternative value, exploring the calculation reinforces understanding that each exterior angle correctly measures 45 degrees, reflecting the geometric properties of the octagon's structure.