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To find the sum of the interior angle measures in an octagon, we use the formula for the sum of interior angles of any polygon:

\[
S = 180(n - 2)
\]

where \( n \) is the number of sides of the polygon.

For an octagon, \( n = 8 \). Plugging this value into the formula:

\[
S = 180(8 - 2) = 180 \times 6 = 1080^\circ
\]

So, the sum of the interior angle measures in an octagon is \( 1080^\circ \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the measure of each interior angle in a regular octagon?
2. How would the sum of angles change if the polygon had 10 sides?
3. What is the sum of the exterior angles in any polygon?
4. How can you determine the number of diagonals in an octagon?
5. What is the relationship between interior and exterior angles in a regular polygon?

**Tip:** The sum of the exterior angles of any polygon is always \(360^\circ\), no matter how many sides the polygon has.

What is the sum of the angle measures in an octagon?

Find out how to calculate the sum of the interior angle measures in an octagon using the polygon angle sum formula. Suitable for middle school students in Grades 6-8.

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