To find the sum of the measures of the interior angles of an octagon, we use the formula for the sum of the interior angles of a polygon, which is given by:
[tex]\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \][/tex]
where [tex]\( n \)[/tex] is the number of sides of the polygon.
For an octagon, [tex]\( n = 8 \)[/tex].
Now, let's substitute [tex]\( n = 8 \)[/tex] into the formula:
[tex]\[ \text{Sum of interior angles} = (8 - 2) \times 180^\circ \][/tex]
[tex]\[ \text{Sum of interior angles} = 6 \times 180^\circ \][/tex]
[tex]\[ \text{Sum of interior angles} = 1080^\circ \][/tex]
Therefore, the sum of the measures of the interior angles of an octagon is [tex]\( 1,080^\circ \)[/tex]. The correct answer is:
c) [tex]\( 1,080^{\circ} \)[/tex]
