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The sum of the exterior angles of a polygon is 360o. For a dodecagon (12 sides) the exterior angle is 360o / 12 = 30o.

The interior and exterior angles are supplementary and so they sum to 180o; thus the interior angle of a dodecagon is 180o - 30o = 150o.

For an interior angle of 144o, the exterior angle is 180o - 144o = 36o, so there are 360o / 36o = 10 sides (a decagon).

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Q: Vertex angle of regular 12 gon measures 144 degrees?
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