Noise cancelling headphones below $200

Newbie here!
Since I'm attending university and I can't study in a noisy environment, I'm searching for headphones below $200 with noise cancelling. Some thoughts:
  • I could not use open back ones since I would also use them in libraries;
  • I'd prefer over-ear ones;
  • I'd prefer ones with Bluetooth/wireless connectivity, it's not a must;
  • I'd prefer foldable ones;
  • I'd like a known brand, but again, it's not a must;
  • I'd prefer some with a nice design, such as the Sennheiser Momentum wireless or the Sony h.ear on Wireless NC.
I've tried the Bose QC25 and QC35, and I've been fascinated by their noise cancelling. I know those are top of the line models with the best NC technology out there, but, is the other branding technology at least similar to them?
If I had to meet all the requirements, I'd pick the Sony ZX770BN. Are they any good?
If you had another option, please tell me what would be your pick!

May 1, 2020
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Oct 8, 2016
Honestly, you named all of the ones I'd suggest. No one comes close to the Bose QC products in terms of pure noise cancelling. The sennheiser momentums and the Sony h.ears are both good contenders. However, your biggest factor is noise canceling and these are outside your budget, I would highly recommend IEMs. While they don't have active noise canceling, they block out probably 90%+ of all noise if you have a good seal. I would suggest getting Comply ear tips to get maximum isolation and comfort. The choose of actual IEMs is highly up to you on your style of music. I'll post another comment with recommendations. I'll also post another comment that has over the ear options within your budget after I do some research. But remember that a headphone doesn't need active noise cancelation if they have good volume to them unless you prefer not to listen at higher volumes.
Oct 9, 2016
Let's start with the fact that I can not justify spending $300+ on a pair of headphones, so the Bose models and the Momentum Wireless are out of range. I would also like to get a good insulation even at low volumes. So, thank you for your answer, and I'll wait for the following one(s)!