To find the measure of an exterior angle of a regular decagon, 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 decagon is also 360^(∘). A decagon has 10 vertices and 10 exterior angles.
In a regular polygon, all exterior angles are congruent. Therefore, a regular decagon has 10 congruent exterior angles. To find the measure of one of them, we will divide 360^(∘) by 10.
360/10 = 36^(∘)
