If the sum of interior angles of a polygon is 1080
degrees, how many sides does the polygon
have

The sum of the interior angles of a polygon is given by the formula:

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

where:
- \( S \) is the sum of the interior angles,
- \( n \) is the number of sides of the polygon.

Given that \( S = 1080^\circ \), we can substitute this value into the formula and solve for \( n \):

\[
1080 = 180(n - 2)
\]

Dividing both sides by 180:

\[
6 = n - 2
\]

Now, solving for \( n \):

\[
n = 6 + 2 = 8
\]

Therefore, the polygon has **8 sides**, which makes it an **octagon**.

Would you like more details on the calculation? Here are some related questions to explore:

1. What is the formula for the exterior angles of a polygon?
2. How do you calculate the sum of exterior angles of any polygon?
3. Can a polygon have fractional or non-integer sides?
4. What is the relationship between the interior and exterior angles of a polygon?
5. How does the sum of the interior angles change as the number of sides increases?

**Tip:** The sum of the interior angles of a polygon always increases by 180° with each additional side!

If the sum of interior angles of a polygon is 1080 degrees, how many sides does the polygon have?

Learn how to determine the number of sides of a polygon when the sum of its interior angles is 1080 degrees. This problem involves the Interior Angle Sum Theorem and is suitable for students in Grades 6-8. Step-by-step solution included.

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