To find the measure of an exterior angle of a regular 15-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 15-gon is also 360^(∘). A 15-gon has 15 vertices and 15 exterior angles.
In a regular polygon, all exterior angles are congruent. Therefore, a regular 15-gon has 15 congruent exterior angles. To find the measure of one of them, we will divide 360^(∘) by 15.
360/15 = 24^(∘)
