Internal and external angles

An interior angle lies inside a polygon between adjacent sides; an exterior angle lies outside it between one side and the extension of an adjacent side.

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Interior angle sum: The sum of a polygon’s interior angles is (n−2) × 180° for an n-sided polygon. It follows by dividing the polygon into triangles, giving a total across all interior angles.
Angle: An angle measures the rotation between two rays sharing a common endpoint. Interior and exterior angles are specific arrangements of rays at polygon vertices.
Convex polygon: A convex polygon has no interior angle greater than 180° and contains every segment joining two of its points. Its exterior angles have a consistent turning direction and sum to 360°.
Reflex angle: A reflex angle measures more than 180° and less than 360°. A concave polygon’s interior angle can be reflex, unlike the usual convex-polygon case.
Exterior angle sum: The signed exterior angles of a convex polygon sum to 360° when measured consistently around it. Turning once around the polygon accumulates one full revolution of exterior angles.
Polygon: A polygon is a closed plane figure formed from a finite sequence of straight line segments. Its vertices and sides determine where interior and exterior angles are measured.
Concave polygon: A concave polygon has at least one interior angle greater than 180°. Its reflex interior angle produces a negative signed exterior turn under the usual convention.
Directed angle: A directed angle records rotation from one ray to another with an orientation and, often, a sign. Signed conventions distinguish an exterior turn from the undirected angle between two lines.
Linear pair: A linear pair is two adjacent angles whose noncommon sides form a straight line. An interior angle and its adjacent exterior angle form a linear pair and sum to 180°.
Vertex: A vertex is a point where two or more lines, edges, or rays meet. Each polygon vertex is the common endpoint of the sides forming its angles.