To find the measure of an exterior angle of a regular 12-gon, we will first recall an important piece of information.
Exterior Angles of a Polygon
In a polygon, the sum of the measures of the exterior angles — one at each vertex — is 360^(∘).
This means that the sum of the exterior angles of a regular 12-gon is also 360^(∘). A 12-gon has 12 vertices and 12 exterior angles.
In a regular polygon, all exterior angles are congruent. Therefore, a regular 12-gon has 12 congruent exterior angles. To find the measure of one of them, we will divide 360^(∘) by 12.
360/12 = 30^(∘)
