A dodecagon is a polygon with twelve sides, with the prefix being a Greek numeral representing the number of sides. The interior angles of a regular dodecagon measure 150°, while the exterior angles measure 30°. The 10 triangles formed by the diagonals of a regular dodecagon are congruent. The sum of interior and exterior angles in a dodecagon is 12 x 150° = 1800°.
In an irregular dodecagon, not all 12 sides are equal. To find the measure of each individual interior angle in a regular dodecagon, divide the sum of the angles by the number of sides: 1800 degrees / 12 = 150 degrees. This means that each interior angle of a regular dodecagon measures 150 degrees.
The formula for finding the total number of degrees of all interior angles is 360 degrees divided by the number of sides: 1800 degrees / 12 = 150°. The central angle of a regular dodecagon is 30 degrees. In conclusion, the measure of the interior angle of a regular dodecagon is 150 degrees. This is because a regular dodecagon is a 12-sided polygon with 12 equal sides, each measuring 120 degrees.
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