Question 37
Let $K$ be a point inside the triangle $A B C$. Let $M$ and $N$ be points such that $M$ and $K$ are on opposite sides of the line $A B$, and $N$ and $K$ are on opposite sides of the line $B C$. Assume that
$$
\angle M A B=\angle M B A=\angle N B C=\angle N C B=\angle K A C=\angle K C A .
$$
Show that $M B N K$ is a parallelogram.
$$
\angle M A B=\angle M B A=\angle N B C=\angle N C B=\angle K A C=\angle K C A .
$$
Show that $M B N K$ is a parallelogram.