What is the sum of the measures of the interior angles of a 12-gon?

Solution:

Given that the polygon has 12 sides.

A 12-sided polygon is called a dodecagon.

A regular dodecagon has all the 12 sides of equal length, all angles of equal measure, and the vertices are equidistant from the center.

The interior angle of a regular dodecagon is calculated by using the formula:

(180n - 360)/n , where n = the number of sides of the polygon.

Here, n = 12

= [(180 × 12) - 360]/12

= 150°

Sum of all interior angles of a polygon of n sides is (n - 2) × 180°

Therefore, the sum of all interior angles = (12 - 2) × 180° = 1800°

What is the sum of the measures of the interior angles of a 12-gon?

Summary:

The sum of the measures of the interior angles of a 12-gon is 1800°.