10,11

In the pyramid $ABCD$, the angle $ABC$ is equal to $\alpha$. Find the angle between the lines, one of which passes through the midpoints of edges $AC$ and $BC$, and the other through the midpoints of edges $BD$ and $CD$.
Let $M, N, K$ and $L$ be the midpoints of segments $A C, B C, B D$ and $C D$ respectively. By the midline theorem of a triangle, $M N \| A B$ and $K L \| B C$. By definition, the angle between lines cannot be greater than $90^{\circ}$, so if angle $A B C$ is acute or right, the angle between lines $M N$ and $K L$ is $\alpha$, if angle $A B C$ is obtuse, then the angle between lines $M N$ and $K L$ is $180^{\circ}-\alpha$.

## Answer

$\alpha$ or $180^{\circ}-\alpha$.