What is the measure of each interior angle in a regular dodecagon?

Each interior angle in a regular dodecagon measures 150 degrees.

A regular dodecagon is a twelve-sided polygon where all sides and angles are equal. To find the measure of each interior angle, you can use the formula for the interior angle of a regular polygon: \((n-2) \times 180^\circ / n\), where \(n\) is the number of sides. For a dodecagon, \(n = 12\).

First, calculate the sum of the interior angles of the dodecagon. Using the formula \((n-2) \times 180^\circ\), we get:
\[
(12-2) \times 180^\circ = 10 \times 180^\circ = 1800^\circ
\]
This means the total sum of all interior angles in a dodecagon is 1800 degrees.

Next, to find the measure of each interior angle in a regular dodecagon, divide the total sum by the number of sides (12):
\[
1800^\circ / 12 = 150^\circ
\]
Therefore, each interior angle in a regular dodecagon measures 150 degrees.

Understanding this concept is crucial for solving various problems in geometry, especially those involving polygons. Remember, the key steps are to find the total sum of the interior angles and then divide by the number of sides to get the measure of each angle. This method can be applied to any regular polygon, not just a dodecagon.