Desde Puno, podemos tomar el tren a Cusco, la cual se supone es Hermosa,

From Puno we can take the train to Cusco, which is supposed to be beautiful,

The phrase is correct as I found all kinds of examples on the web. It just seems strange to me to see "se supone" and then a conjugated verb (es) directly afterwards. Ah, maybe it's something like the following:
- la cual es hermosa (se supone)
 

Steven, I think you hit on the head with ​se pone​ being a parenthetical phrase in nature.  It can also mean, "one supposes."

Steven: I like these little grammatical conundrums you have been posting. However, I was able to work this one out and it made sense to me. Which worries me, since you found it puzzling.

Taking the train from Cusco to visit Machu Picchu has long been on my "Someday I Will" list. 

Worried? Dude! You're the man here in the Spanish forum.

I actually did understand the phrase but couldn't understand why when I looked closer at the verb conjugations. the-hefay confirmed what I suspected: Desde Puno, podemos tomar el tren a Cusco, la cual (se supone) es Hermosa...
 

I am on this lesson and phrase this morning, but I have a different question.  
"...la cual se supone es Hermosa,"
Why are they using the feminine?   
Is it a throwback to other dialog, where they have been referring to "la ciudad", or just an unspoken that Cusco is a city (la ciudad), or is there a different rule?  
I've seen this before, and wondered why, particularly when defaults in Spanish normally seem to lean to the masculine.  

(and why capitalize Hermosa?)

I think I got this one (I thought this discussion looked familiar). Spanish does default to the masculine when the context is ambiguous but here hermosa definitely corresponds to la cual which in turn refers to Cusco la ciudad as you mention.

I wouldn't pay too much attention to the capitalization and punctuation used in the course - I've found it to be a bit "loose". I used to send in corrections for stuff like this but I got the impression that RL wasn't all that interested in those details.

Has it been a year already since I asked that question? Where does the time go...
 

Steven, I'm in agreement with you.  I did run it by my wife and she said you were correct.  That being said, in regards to Cusco, one could use the masculine.  Many times, depending on the context, Cusco is el Cusco.  

I thought the same thing about the time flying by when I noticed it was a year ago that you posted this.  I would've said it was only a few months ago.

I discovered this in French with Cairo: le Caire (curiously enough, it's also el Cairo in Spanish - must be a Latin carry over). To avoid such cases, I would say something to the effect of Cairo, that city is... which would always follow with a feminine adjective. Cheating perhaps but it seems to work.

[Ahora que pienso en ello, es lo mismo en árabe: el qahirah (لقاهرة‎ ).] 
 

nothing wrong with cheating.  :)