To determine the measure of each exterior angle of a regular heptagon, we can follow these steps:
1. Understand the properties of a heptagon:
- A heptagon is a seven-sided polygon.
2. Formula for the exterior angle:
- The measure of each exterior angle of a regular polygon with [tex]\( n \)[/tex] sides is given by the formula:
[tex]\[
\text{Exterior angle} = \frac{360^\circ}{n}
\][/tex]
- For a heptagon, [tex]\( n = 7 \)[/tex].
3. Calculate the exterior angle:
- Substitute [tex]\( n = 7 \)[/tex] into the formula:
[tex]\[
\text{Exterior angle} = \frac{360^\circ}{7}
\][/tex]
- By performing the division, we get:
[tex]\[
\text{Exterior angle} \approx 51.42857142857143^\circ
\][/tex]
4. Rounding to the nearest degree:
- When we round [tex]\( 51.42857142857143^\circ \)[/tex] to the nearest whole number, we get [tex]\( 51^\circ \)[/tex].
So, to the nearest degree, the measure of each exterior angle of a regular heptagon is [tex]\( 51^\circ \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{51^\circ} \)[/tex].
