To find the measure of one interior angle of a regular 15-gon, follow these steps:
1. Understand the formula: The measure of an interior angle of a regular [tex]\(n\)[/tex]-gon (a polygon with [tex]\(n\)[/tex] sides) can be calculated using the formula:
[tex]\[
\text{Interior angle} = \frac{(n - 2) \times 180^\circ}{n}
\][/tex]
In this formula:
- [tex]\(n\)[/tex] is the number of sides of the polygon.
- The expression [tex]\((n - 2) \times 180^\circ\)[/tex] calculates the sum of the interior angles of the polygon.
- Dividing this sum by [tex]\(n\)[/tex] gives the measure of one interior angle, because all interior angles in a regular polygon are equal.
2. Substitute the number of sides: For a 15-gon, [tex]\(n = 15\)[/tex]. Plugging in this value:
[tex]\[
\text{Interior angle} = \frac{(15 - 2) \times 180^\circ}{15}
\][/tex]
3. Calculate step-by-step:
[tex]\[
\begin{align*}
(15 - 2) \times 180^\circ &= 13 \times 180^\circ \\
\end{align*}
\][/tex]
This gives:
[tex]\[
13 \times 180^\circ = 2340^\circ
\][/tex]
4. Divide the sum by the number of sides:
[tex]\[
\frac{2340^\circ}{15} = 156^\circ
\][/tex]
Thus, the measure of one interior angle of a regular 15-gon is [tex]\(156^\circ\)[/tex].
Therefore, the correct answer is
C. 156.
