To determine the measure of each exterior angle of a regular 11-gon, we use the property that the sum of the exterior angles of any polygon is [tex]\(360^\circ\)[/tex].
For a regular [tex]\(n\)[/tex]-gon, each exterior angle is equal since the polygon is regular. Therefore, the measure of each exterior angle can be found by dividing the total sum of the exterior angles by the number of sides [tex]\(n\)[/tex].
Given that [tex]\(n = 11\)[/tex] for an 11-gon:
[tex]\[
\text{Measure of each exterior angle} = \frac{360^\circ}{n}
\][/tex]
Substitute [tex]\(n = 11\)[/tex]:
[tex]\[
\text{Measure of each exterior angle} = \frac{360^\circ}{11}
\][/tex]
When we perform the division:
[tex]\[
\frac{360^\circ}{11} \approx 32.727^\circ
\][/tex]
Rounding to the nearest degree:
[tex]\[
32.727^\circ \approx 33^\circ
\][/tex]
Thus, the measure of each exterior angle of a regular 11-gon, rounded to the nearest degree, is [tex]\(33^\circ\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{33^\circ}
\][/tex]
