Problem #PRU-57008

Problems Geometry Plane geometry Polygons Polygons (other)

Problem

a) The convex \(n\)-gon is cut by diagonals that do not cross to form triangles. Prove that the number of these triangles is equal to \(n - 2\).

b) Prove that the sum of the angles at the vertices of a convex \(n\)-gon is \((n - 2) \times 180^{\circ}\).