Certainly! Let's determine the sum of the measures of the interior angles of an octagon by following a clear, step-by-step approach.
1. Concept Understanding:
The sum of the interior angles of a polygon with [tex]\( n \)[/tex] sides can be calculated using the formula:
[tex]\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\][/tex]
2. Identify the Number of Sides:
An octagon has [tex]\( 8 \)[/tex] sides, so [tex]\( n = 8 \)[/tex].
3. Apply the Formula:
Substitute [tex]\( n = 8 \)[/tex] into the formula:
[tex]\[
\text{Sum of interior angles} = (8 - 2) \times 180^\circ
\][/tex]
4. Calculate:
Simplify the expression within the parentheses first:
[tex]\[
8 - 2 = 6
\][/tex]
Then multiply by [tex]\( 180^\circ \)[/tex]:
[tex]\[
6 \times 180^\circ = 1080^\circ
\][/tex]
Hence, the sum of the measures of the interior angles of an octagon is:
[tex]\[
\boxed{1080^\circ}
\][/tex]
Thus, the correct answer is:
D. [tex]\(1080^\circ\)[/tex]
