In a convex polygon, I am inclined to construe the word "diagonal" to mean any of the segments connecting non-adjacent vertices and "edge" to mean any of the segments connecting adjacent vertices.
Is there a standard term that means any of the segments connecting two vertices regardless of whether they are adjacent?
If such a polygon is inscribed in a circle, consider the sequence of angles that includes $(1)$ the angle between a tangent ray and the adjacent edge, and $(2)$ the angle between that edge and the adjacent diagonal, and $(3)$ the angle between that diagonal and the next, $(4)$ and so on, until one reaches the angle between the next edge and the corresponding tangent ray. Proposition: That sequence of angles is the same at every vertex, modulo cyclic shifts. Proof: This is a corollary of your secondary-school geometry course.$\,\,\blacksquare\quad$ Question: Is there a name for that sequence of angles?