Anglesare

Anglesare is a coined term used in mathematics education and puzzle communities to describe a framework for organizing and solving problems based on angle relationships in planar figures. It functions as a practical shorthand rather than a formal theory, helping students and problem-solvers categorize angles and apply established rules.

Definition and scope: Anglesare emphasizes recognizing angle types (vertical, adjacent, corresponding, alternate interior, inscribed) and leveraging sum relations (the triangle sum is 180 degrees; the sum of interior angles of an n-gon is (n−2)×180 degrees; cyclic quadrilateral opposite angles are supplementary). In angle-chasing tasks, practitioners use these relationships to deduce unknown angles from given data. The approach is common in contest problem solving and geometry puzzles, where a structured checklist guides reasoning.

Origin and usage: The term arose in online math communities in the 2010s and 2020s as a colloquial shorthand. It does not denote a distinct branch of geometry but a pedagogical approach to organizing angle facts. Materials labeled as anglesare typically include worked examples, a catalog of angle types, and step-by-step strategies for constructing or deconstructing figures.

See also: Euclidean geometry, angle chasing, polygon angle sum, inscribed angle theorem, cyclic quadrilateral, parallel lines, geometry education.