A question on the requirement of a quadrilateral being an adventitious quadrangle There is a special type of problem called Langley’s Adventitious Angles. See < The problem was solved and has the following generalization:- “A quadrilateral such as BCEF (with a, b, c, d as the 4 interior angles) in which **the angles formed by all triples of vertices are rational multiples of π** is called an adventitious quadrangle.” I don’t quite understand the meaning of words in bold. An illustrative example would be nice.

It means that if $X$, $Y$, $Z$ are any three of $B,C,E,F$ then $\angle XYZ$ has measure (in radians) of the shape $r\pi$ for some rational number $r$. Equivalently, since $\pi$ radians is $180^\circ$, it means that every angle is a rational number of degrees. Thus angles like $\frac{99}{7}$ degrees or $17$ degrees are OK, but (for example) an angle of $20\sqrt{2}$ degrees is not.