Question 18
$ABCD$ is a quadrilateral with $AB=BC=CD=DA$ and $\angle ABC\lt 90^\circ$. Points $E$ and $F$ are on lines $BC$ and $CD$, respectively, and
$$AB=AE=AF=FE.$$
Find $\angle BEF$, using the interior-point convention stated below.
The printed wording says “on lines”, which allows extensions and does not determine a unique angle. For the main answer, explicitly assume $E$ and $F$ lie strictly inside sides $BC$ and $CD$, respectively. The solution explains the ambiguity of the literal wording.
$$AB=AE=AF=FE.$$
Find $\angle BEF$, using the interior-point convention stated below.
The printed wording says “on lines”, which allows extensions and does not determine a unique angle. For the main answer, explicitly assume $E$ and $F$ lie strictly inside sides $BC$ and $CD$, respectively. The solution explains the ambiguity of the literal wording.