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I found a free Trek dumpster bike with a broken mangled derailleur. It was ripped in half! And the derailleur hanger was twisted around almost 45 degrees. The bike was trashed, but hey, it was free! I am guessing the derailleur hit something, and the cage was torn from the body. Maybe the cage got caught in the spokes, though no spokes seemed damaged. I am just guessing. Anyway, I managed to straighten the hanger, and replaced the derailleur with a similar model. I also replaced the rusty chain. The bike will come back to life. The bike is a Trek 820.

This is the derailleur hanger alignment tool I used (Park Tool DAG 2.2):
https://www.amazon.com/exec/obidos/ASIN/B010T6L22E/ref=nosim/youtube25-20

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