To find the measure of each exterior angle of a regular octagon, follow these steps:
1. Identify the key fact about polygons: For any polygon, the sum of the measures of its exterior angles is always [tex]\(360^\circ\)[/tex].
2. Know the number of sides in a regular octagon: A regular octagon has 8 sides.
3. Calculate the measure of each exterior angle: Since the exterior angles of a regular polygon are all equal, you can find the measure of each exterior angle by dividing the total sum of the exterior angles by the number of sides.
Mathematically, this can be expressed as:
[tex]\[
\text{Measure of each exterior angle} = \frac{\text{Sum of exterior angles}}{\text{Number of sides}}
\][/tex]
For an octagon:
[tex]\[
\text{Measure of each exterior angle} = \frac{360^\circ}{8}
\][/tex]
4. Perform the division:
[tex]\[
\frac{360^\circ}{8} = 45^\circ
\][/tex]
5. Round to the nearest degree: In this case, the calculation yields exactly [tex]\(45^\circ\)[/tex], so rounding is not necessary.
Thus, the measure of each exterior angle of a regular octagon, rounded to the nearest degree, is [tex]\(45^\circ\)[/tex].
The correct answer is:
A. [tex]\(45^\circ\)[/tex]
