The minimum possible interior angle in a regular polygon can be determined by using the formula for the interior angles of a polygon.

Formula for the interior angles of a polygon:
The sum of the interior angles of a polygon can be calculated using the formula:

Sum of interior angles = (n - 2) * 180 degrees

Where n represents the number of sides of the polygon.

Explanation:
In a regular polygon, all sides and angles are equal. Therefore, to find the measure of each interior angle, you divide the sum of the interior angles by the number of sides.

Let's consider a regular polygon with n sides. The formula for each interior angle can be written as:

Each interior angle = (Sum of interior angles) / n

To find the minimum possible interior angle, we need to find the smallest value for n that still forms a regular polygon. The smallest regular polygon is a triangle (n = 3).

Using the formula for the sum of interior angles, we can calculate the sum of angles for a triangle:

Sum of interior angles = (n - 2) * 180 degrees
= (3 - 2) * 180 degrees
= 1 * 180 degrees
= 180 degrees

Now, we can calculate the measure of each interior angle:

Each interior angle = Sum of interior angles / n
= 180 degrees / 3
= 60 degrees

Therefore, the minimum possible interior angle in a regular polygon is 60 degrees.