Find the sum of the measures of interior angles and the sum of the measures of the exterior angles of a regular dodecagon (12 sided figure)

Question

Find the sum of the measures of interior angles and the sum of the measures of the exterior angles of a regular dodecagon? (12 sided figure)

Answer 1

Rachel,

Two key ingredients are involved in this type of problem: #1 interior and exterior angles of any regular polygon are calculated differently - #2 there is a specific rule/formula available for each.

 

When calculating the exterior angle measurements of REGULAR polygons: adding ALL the exterior angles added together will yield 360º. So whether you have 3 sides of 333 sides (or vertices), they will all sum to equal 360º. If you want to calculate the angular measurement of one single exterior angle, just divide 360º by the number of sides (or vertices).

 

To calculate the measures of the interior angles of REGULAR polygons, follow this specific formula. (n - 2) • 180 where n = the number of sides (or vertices) of the specific regular polygon. In this case, n = 12, so (12 - 2) • 180º = 1800º.

 

Hope this helps!

 

Neal