How to show that a line graph of a graph L(G) has a Euler cycle if the original graph G has a Euler cycle?

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The line graph $L(G)$ of a graph $G$ has a vertex for each edge of $G$, and two of these vertices are adjacent if and only if the corresponding edges in $G$ have a common end vertex.

  • (a) Show that $L(G)$ has an Euler cycle if $G$ has an Euler cycle.

  • (b) Find a graph $G$ that has no Euler cycle but for which $L(G)$ has an Euler cycle.

I just need a hint here.

What theorems do I use to show (a)?

If I can understand (a) I can definitely do (b) on my own