https://file.aiquickdraw.com/mathbot/file/1730363559659ybbrvkjt.jpg

To find the number of sides \( n \) of a regular polygon given that each interior angle is 162°, we can use the formula for the interior angle of a regular polygon:

\[
\text{Interior angle} = \frac{(n - 2) \times 180^\circ}{n}
\]

### Step 1: Set up the equation
Since we know the interior angle is 162°, we can set up the equation:

\[
\frac{(n - 2) \times 180}{n} = 162
\]

### Step 2: Solve for \( n \)
1. Multiply both sides by \( n \) to eliminate the fraction:
   \[
   (n - 2) \times 180 = 162n
   \]

2. Distribute 180 on the left side:
   \[
   180n - 360 = 162n
   \]

3. Move all terms involving \( n \) to one side:
   \[
   180n - 162n = 360
   \]

4. Simplify:
   \[
   18n = 360
   \]

5. Divide by 18:
   \[
   n = 20
   \]

### Conclusion
The polygon has **20 sides**.

Would you like further details or have any questions?

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Here are five related questions for further exploration:
1. How would the solution change if each interior angle was 150°?
2. What is the formula for the exterior angle of a regular polygon?
3. Can a polygon have an interior angle of 90°? If so, what shape would it be?
4. How can we determine the sum of interior angles of a polygon with 20 sides?
5. What would be the measure of each exterior angle of this polygon?

**Tip:** The exterior angle of a regular polygon can be easily calculated by dividing 360° by the number of sides \( n \).

The diagram shows part of a regular polygon. Each interior angle is 162°. Find the number of sides of the polygon.

This page provides a step-by-step solution to finding the number of sides in a regular polygon given each interior angle is 162°. Learn the formula and concepts used in solving polygon-related geometry problems, suitable for Grades 8-10.

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