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?

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 $n$.