Geometry · Polygon angle sum · Reflex angle · Non convex polygon · Extremal example
At most how many interior angles of a polygon with \(n\) vertices can be greater than \(180^\circ\)? (The polygon is simple: its sides meet only at the shared endpoints of neighbouring sides.)
- A \(n - 1\)
- B \(n - 2\)
- C \(n - 3\)
- D \(n - 4\)
- E \(n - 5\)
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), regijsko (regional) round 2012, 1. letnik, category A, problem A2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source