Is there any way to get a specific angle using the knife tool? Instead of the constrained 45 degrees that happens when you press C, is there a specific angle I can get for example 35 degrees instead? 

It's currently cut at 45 degrees in the attached image and I need it to be 35.
This is a work around.
For a simple object like your cylinder, simply rotate it in object mode 35°, make the cut, then rotate the object back.


For more complex objects where you can not rotate it. You can align the view to a rotated face. You could duplicate a face out of your mesh and separate it in to a new object, or just add a new object, a plane or an empty; then align the view to it with  with ShiftNumPad 7.



Finally do not forget that you can roll the view, but that is limited to 15° increments.