To find the measure of one interior angle of a regular octagon, you can use the formula for the interior angle of a regular polygon:
[tex]\[
\text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n}
\][/tex]
where [tex]\( n \)[/tex] is the number of sides in the polygon. For a regular octagon, [tex]\( n = 8 \)[/tex].
Let's calculate this step by step:
1. Substitute the value of [tex]\( n \)[/tex] into the formula:
[tex]\[
\text{Interior Angle} = \frac{(8-2) \times 180^\circ}{8}
\][/tex]
2. Simplify the numerator:
[tex]\[
8 - 2 = 6
\][/tex]
[tex]\[
\text{Interior Angle} = \frac{6 \times 180^\circ}{8}
\][/tex]
3. Multiply 6 by 180:
[tex]\[
6 \times 180^\circ = 1080^\circ
\][/tex]
4. Divide by 8:
[tex]\[
\text{Interior Angle} = \frac{1080^\circ}{8} = 135^\circ
\][/tex]
Therefore, the measure of one interior angle of a regular octagon is [tex]\( \boxed{135^\circ} \)[/tex].
So, the answer is:
B. 135
