$L$ is submanifold of $\mathbb{R}^n$ with $\dim L\leq n-2$.

Question

Suppose $L$ is submanifold of $\mathbb{R}^n$ with $\dim L\leq n-2$. Prove that

1. If $x\notin L$, then for almost every line $l$ passing $x$, $l \cap L=\phi$;
2. If $x\in L$, then for almost every line $l$ passing $x$, $l \cap L=\{x\}$.

I am currently learing the Transversality Theorem with parameters. I feel we need to prove for almost every line passing $x$, $l \pitchfork L$, but I do not know how to start.

Appreciate any help! If you may, please give a clear statement of the theorems you use.