To find the measure of one interior angle of a regular polygon, we use the formula for the interior angle:
[tex]\[
\text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n}
\][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon. In this case, we need to find the measure of one interior angle of a regular 7-gon, which means [tex]\( n = 7 \)[/tex].
1. Substitute the given number of sides (7) into the formula:
[tex]\[
\text{Interior Angle} = \frac{(7-2) \times 180^\circ}{7}
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
7 - 2 = 5
\][/tex]
3. Multiply by 180 degrees:
[tex]\[
5 \times 180^\circ = 900^\circ
\][/tex]
4. Divide by the number of sides (7):
[tex]\[
\frac{900^\circ}{7} \approx 128.57142857142858^\circ
\][/tex]
After calculating, the measure of one interior angle of a regular 7-gon is approximately 128.6 degrees.
Therefore, the correct answer is:
D. 128.6
