To find the measure of one interior angle of a regular 14-gon, we can use the formula for calculating the interior angle of a regular polygon. The formula is:
[tex]\[ \text{interior angle} = \frac{(n - 2) \times 180^\circ}{n} \][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon.
Let's go through the steps:
1. Identify the number of sides of the polygon. In this case, it is a 14-gon, so [tex]\( n = 14 \)[/tex].
2. Substitute [tex]\( n = 14 \)[/tex] into the formula:
[tex]\[
\text{interior angle} = \frac{(14 - 2) \times 180^\circ}{14}
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
14 - 2 = 12
\][/tex]
4. Multiply the result by 180 degrees:
[tex]\[
12 \times 180^\circ = 2160^\circ
\][/tex]
5. Finally, divide by the number of sides ([tex]\( n = 14 \)[/tex]):
[tex]\[
\text{interior angle} = \frac{2160^\circ}{14} \approx 154.28571428571428^\circ
\][/tex]
Therefore, the measure of one interior angle of a regular 14-gon is approximately 154.28571428571428 degrees.
Looking at the provided options:
A. 140
B. 154.3
C. 160
D. 150
The closest option to our answer is:
B. 154.3
