To determine the measure of an exterior angle of a regular convex polygon, you can use the formula for the measure of an exterior angle:
[tex]\[ \text{Exterior Angle} = \frac{360^\circ}{n} \][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon.
Given that the polygon has eight sides ([tex]\( n = 8 \)[/tex]), we can apply the formula:
[tex]\[ \text{Exterior Angle} = \frac{360^\circ}{8} = 45^\circ \][/tex]
So, the measure of an exterior angle of a regular convex polygon with eight sides is [tex]\( 45^\circ \)[/tex].
Therefore, the correct answer is:
B. 45°
