Each interior angle in a regular dodecagon measures $150^\circ$.

A regular dodecagon is a polygon with twelve sides, where all sides and angles are equal. To determine the measure of each interior angle, we can use the formula for the interior angle of a regular polygon, which is given by:

Here, $n$ represents the number of sides. For a dodecagon, we have $n = 12$.

First, we calculate the total sum of the interior angles of the dodecagon using the formula:

Plugging in the value for $n$:

This indicates that the total sum of all interior angles in a dodecagon is $1800^\circ$.

Next, to find the measure of each interior angle in a regular dodecagon, we divide this total sum by the number of sides (which is $12$):

Consequently, each interior angle in a regular dodecagon measures $150^\circ$.

Grasping this concept is essential for tackling various geometric problems, particularly those involving polygons. Remember, the key steps are to compute the total sum of the interior angles and then divide by the number of sides to ascertain the measure of each angle. This approach can be applied to any regular polygon, not just a dodecagon.