Geometry

Question Analysis

This question involves the characteristics of regular polygons. The main focus is on understanding the relationship between the number of sides of a regular polygon and the measure of its interior angles.

 

Key Concept Explanation

The sum of the interior angles of a polygon can be found using the formula , where is the number of sides of the polygon. For a regular polygon, all interior angles are equal. So, to find the measure of one interior angle, we divide the sum of the interior angles by the number of sides .

 

Step - by - Step Solution

For a dodecagon with , first find the sum of the interior angles using the formula .

The sum of the interior angles is .

Since a dodecagon is regular, all interior angles are equal. So the measure of one interior angle is

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