https://file.aiquickdraw.com/mathbot/file/17333370274886d9qacg5.jpg

To solve the problem, we use the formula for the sum of the interior angles of a polygon:

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

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

Given \( S = 1620^\circ \), substitute it into the formula:

\[
1620 = 180(n - 2)
\]

Solve for \( n \):

1. Divide both sides by 180:
\[
n - 2 = \frac{1620}{180}
\]

\[
n - 2 = 9
\]

2. Add 2 to both sides:
\[
n = 11
\]

Thus, the polygon has **11 sides**.

Let me know if you have any questions or need further clarification.

### Follow-Up Questions:
1. What is the formula to calculate the sum of interior angles for any polygon?
2. How do you determine the measure of each interior angle for a regular polygon?
3. What is the sum of the interior angles of a decagon (10 sides)?
4. How does the sum of exterior angles of any polygon relate to its interior angles?
5. Can this method be used for non-convex polygons?

### Tip:
For any polygon, the sum of its **exterior angles** is always \(360^\circ\), regardless of the number of sides!

The sum of the interior angle measures of a convex polygon is 1620°. How many sides does it have?

Solve for the number of sides of a convex polygon with a sum of interior angles equal to 1620°. This problem utilizes the polygon angle-sum formula S = 180(n - 2) and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation