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The problem asks for the formula to find the sum of the interior angles of a polygon with \( n \) sides. 

The general formula for the sum of the interior angles of a polygon is:

\[
S = (n - 2) \times 180^\circ
\]

Where:
- \( n \) is the number of sides of the polygon.
- \( 180^\circ \) comes from the fact that the sum of angles in a triangle is \( 180^\circ \), and a polygon can be divided into \( n - 2 \) triangles.

Now, looking at the options:

- \( \text{A:} \ (n - 2) \times 360^\circ \) — Incorrect.
- \( \text{B:} \ (n - 3) \times 360^\circ \) — Incorrect.
- \( \text{C:} \ (n - 2) \times 180^\circ \) — **Correct.**
- \( \text{D:} \ (n - 2) \times 90^\circ \) — Incorrect.
- \( \text{E:} \ (n - 3) \times 180^\circ \) — Incorrect.

Thus, the correct answer is **C: \( (n - 2) \times 180^\circ \)**.

Would you like further explanation or any additional details?

Here are 5 related questions:
1. What is the sum of the interior angles of a hexagon (6-sided polygon)?
2. How do you calculate the measure of each interior angle in a regular polygon?
3. What is the difference between interior and exterior angles of polygons?
4. Can a polygon have an interior angle sum greater than 1800°? Why or why not?
5. How many sides does a polygon have if the sum of its interior angles is 1080°?

**Tip:** To find the measure of each interior angle in a regular polygon, divide the sum of the interior angles by the number of sides.

The sum of the measures of the interior angles of a polygon with n sides is:

Learn how to calculate the sum of the interior angles of a polygon with n sides using the formula (n - 2) × 180°. Understand key concepts in geometry and apply the Polygon Interior Angle Sum Theorem. Suitable for students in Grades 8-10.

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