To find the number of sides of a regular polygon when each interior angle measures 162°, we can use the following relationship between the number of sides ($n$) and the measure of each interior angle:

$\text{Interior angle} = \frac{(n-2) \times 180}{n}$

In this case, the interior angle is given as 162°. We can set up the equation:

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

Now, solve for $n$:

1. Multiply both sides by $n$ to eliminate the fraction: $162n = (n-2) \times 180$

2. Expand the right-hand side: $162n = 180n - 360$

3. Move all terms involving $n$ to one side: $162n - 180n = -360$

4. Simplify: $-18n = -360$

5. Solve for $n$: $n = \frac{360}{18} = 20$

So, the polygon has 20 sides.

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Would you like me to explain any part of the solution in more detail? Here are some follow-up questions:

1. What is the exterior angle of a polygon with 20 sides?
2. How can you calculate the sum of the interior angles of a polygon?
3. What is the relationship between the interior and exterior angles of a regular polygon?
4. How do you find the number of sides of a polygon if the exterior angle is known?
5. What is the formula for the exterior angle of a regular polygon?

Tip: To check your answer, remember that the sum of the interior angles of a polygon with $n$ sides is $(n-2) \times 180$.