Question 81
Let $ABCD$ be a parallelogram such that the projections $K$, $L$ of $D$ onto the sides $AB$, $BC$, respectively, are their interior points. Prove that $KL \parallel AC$ if and only if
$$
\angle BCA + \angle ABD = \angle BDA + \angle ACD.
$$
$$
\angle BCA + \angle ABD = \angle BDA + \angle ACD.
$$