Prove that in a planar graph, every edge in a cycle touches two faces.

[last mesa]

1. Do not ping the Moderators, unless someone is breaking the rules.
2. Do not ping the Helper Moderators, unless there is a conflict between helpers.
3. Do not ping other members randomly for help.
4. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
5. Wait patiently for a helper to come along.
6. If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:

+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[bitter bolt]

Also we can't use Euler's identity because I proved it with this lemma.

I guess I can prove Euler without using this lemma

though I wonder how I should do it without using Euler

[toxic mica]

I mean, a cycle is a face, right?

Or bounds a face?