It is in the angle itself because in an angle there is the interior (part) the inside of the angle and the exterior (part) outside the angle and the angle itself so the vertex is in the angle it self it is neither exterior or interior
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It is: 180-vertex angle = exterior angle
The sum of the exterior angles of a convex polygon which has sides and one angle at each vertex is 360 degrees.
The total interior angle of a 12 sided polygon is = (12 - 2) 180 degrees = 1800 degrees. The internal angle at each vertex of an regular dodecagon is equal to = = 150 degrees. While the exterior angle at a single vertex is = = 30 degrees. The total exterior angle of a 12 sided polygon is 360 degrees.
The exterior angles of a polygon always total 360 degrees. That doesn't even depend on how many sides the polygon has.
Exterior angle+interior angle=180 degrees and 180-exterior angle=interior angle