To determine the measure of an interior angle of a regular 15-gon, we need to follow these steps:
1. Understand the Problem:
We are dealing with a regular polygon, specifically a 15-sided polygon (15-gon). A regular polygon means all sides and all interior angles are equal.
2. Identify the Relevant Formula:
The measure of an interior angle of a regular polygon can be found using the formula:
[tex]\[
\text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n}
\][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon.
3. Substitute the Given Values:
In our scenario, [tex]\( n = 15 \)[/tex]. Plugging in 15 for [tex]\( n \)[/tex] in the formula gives:
[tex]\[
\text{Interior Angle} = \frac{(15 - 2) \times 180^\circ}{15}
\][/tex]
4. Simplify the Expression:
First, subtract within the numerator:
[tex]\[
15 - 2 = 13
\][/tex]
Then, perform the multiplication:
[tex]\[
13 \times 180^\circ
\][/tex]
And the result is:
[tex]\[
2340^\circ
\][/tex]
Now, divide by the number of sides, 15:
[tex]\[
\frac{2340^\circ}{15} = 156^\circ
\][/tex]
5. Conclusion:
The measure of an interior angle of a regular 15-gon is therefore:
[tex]\[
\boxed{156^\circ}
\][/tex]
Among the given options, the correct choice is:
- [tex]\[
156^\circ
\][/tex]
