Introduction:
To determine the number of sides of a regular polygon, we can use the formula for the interior angle of a regular polygon. The interior angle of a regular polygon can be found using the formula:

Interior Angle = (n-2) * 180 / n

Where n represents the number of sides in the polygon.

Given:
In this problem, we are given that the interior angle of the polygon is 162 degrees.

Substitute the given values:
We can substitute the given interior angle into the formula and solve for n:

162 = (n-2) * 180 / n

Solve for n:
To solve for n, we can cross multiply and simplify the equation:

162n = 180n - 360
-18n = -360
n = -360 / -18
n = 20

Answer:
The polygon has 20 sides.

Explanation:
The formula for the interior angle of a regular polygon is derived from the fact that the sum of all interior angles of any polygon is equal to (n-2) * 180 degrees, where n is the number of sides. Since a regular polygon has all angles congruent, we can divide the sum of the interior angles by the number of sides to find the measure of each interior angle.

In this case, we are given that the interior angle of the polygon is 162 degrees. By substituting this value into the formula and solving for n, we find that the polygon has 20 sides.

Thus, the regular polygon in question has 20 sides.