Interior angle

An interior angle is formed inside a polygon by two adjacent sides meeting at a vertex. Its measure depends on the polygon’s shape.

Polygon: A closed plane figure bounded by finitely many straight line segments. Interior angles are defined at the vertices of polygons.
Interior angle sum: The total of the interior-angle measures of a polygon. It links an individual interior angle to the polygon’s total angular measure.
Tessellation: A covering of a plane with shapes that fit together without gaps or overlaps. Angles around each tiling vertex must combine to a full turn.
Reflex angle: An angle measuring more than 180 degrees and less than 360 degrees. A polygon’s interior angle can be reflex at a concave vertex, but not at a convex one.
Vertex (geometry): A point where two or more geometric lines, segments, or edges meet. The two adjacent sides forming an interior angle meet at a polygon vertex.
Exterior angle: An angle formed outside a polygon by one side and the extension of an adjacent side. It lies outside the polygon, unlike the interior angle at the same vertex.
Compass-and-straightedge construction: A geometric construction using only an unmarked straightedge and a compass. Constructing regular polygons requires controlling their interior angles.
Concave polygon: A simple polygon with at least one interior angle greater than 180 degrees. Its reflex interior angle distinguishes it from a convex polygon.
Adjacent sides: Sides of a polygon that share a common endpoint. An interior angle is bounded by the adjacent sides meeting at its vertex.
Triangle: A polygon with three sides and three interior angles. Every triangle’s interior angles sum to 180 degrees.

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