Can anyone tell me what temperature the numbers on my Hanger 9 Heat Iron represent? The settings are Lo, 1-5 and high. I am surprised that Hanger 9 did not include this in with their iron.

There is available a little disc that you lay on the iron and it gives the exact temp of the iron. Temp settings on an iron are not accurate depending on if your using a sock or bare iron.

I did buy a sock to go on it.

I don't understand why whoever manufactured the iron for Hanger 9 could not have performed a temperature test and listed the results. How simple would it have been for them to say OK, put iron on number 2 and it will be about 200 degrees F., on #3 and it'll be about 300 degrees F. and so forth. Having to go out and buy yet another tool just so you can find out what the hell the first tool is doing is absurd.

Yes. I find the Century 21 iron with the proper control best. But only after buying the Hangar 9 first. Waste of money as the temp control doesn't seem as tight either.

It is not a waste of money. The Hanger 9 iron will work just fine.
You do not need to buy a temperature disk, either.
Just use it and you will learn what settings are correct. You need to practice with it anyway.
Lighten up and enjoy the insanity.