To determine the sum of the measures of the interior angles of a regular convex polygon with 14 sides, we use the following geometric principle.
1. Understand the formula: The sum of the interior angles of a polygon is given by the formula [tex]\((n - 2) \times 180^\circ\)[/tex], where [tex]\(n\)[/tex] is the number of sides of the polygon.
2. Identify the number of sides: For this problem, [tex]\(n = 14\)[/tex].
3. Plug the value into the formula: Substitute [tex]\(n = 14\)[/tex] into the formula:
[tex]\[
(n - 2) \times 180^\circ = (14 - 2) \times 180^\circ
\][/tex]
4. Simplify the equation:
[tex]\[
(14 - 2) = 12
\][/tex]
5. Multiply by 180°:
[tex]\[
12 \times 180^\circ = 2160^\circ
\][/tex]
So, the sum of the measures of the interior angles of a regular convex polygon with 14 sides is [tex]\(2160^\circ\)[/tex].
Therefore, the correct answer is:
A. 2160°
