When you disclose your invention to anyone without some form of protection or reasonable expectation of confidentiality in place, you put yourself at risk. Many angels are not willing to execute NDAs because they look at so many deals and they don't want to be sued by someone they turned down because they invested in someone with a similar idea. You have to look at your situation, the likelihood of the angels being supportive, and evaluate whether the risk is worth it.
If you want additional protection and if you think your IP is novel, file a provisional patent application that at least discloses everything you intend to share with the angel investors. For the provisional to have value down the road, you will need to file the utility application, but as the US is now following first-to-file rules in the Patent Office, having something on file will give you a little extra protection moving forward.
Good luck,
Todd
Answered on Sep 26th, 2013 at 8:45 AM