In an acute triangle $K L M$, $V$ is the intersection of its altitudes and $X$ is the foot of the altitude on side $K L$. The bisector of angle $X V L$ is parallel to side $L M$ and angle $M K L$ has a size of $70^{\circ}$.

What are the sizes of angles $K L M$ and $K M L$?

(L. Hozová)

Hint. Visualize the situation described and look for congruent angles.