I thought the angles were the hardest questions on the PAT. I got 20 on the section.
For me, I did tear a corner from the scratch paper and held it next to the screen. Nobody stopped me, and I haven't heard anythings since. If it was illegal, someone would have warned.
In terms of time... if I used it for every angle question, then of course I will run out of time. However, I used it mainly for the angles that were very very close; so that was helpful.
By the way, the scratch paper are YELLOW. Yes, YELLOW. So, nothing on the screen is transparent through the paper, so what you have to do is to tear a small corner piece from the scratch, not a large one (a large one will simply block the two lines), but if you use a small paper, then, you can still see the two lines protruding out of the teared paper.
Maybe this doesn't make sense, but it is hard, since I'm trying to describe it, but try it. Try tearing small piece of corner paper no bigger than your pinky, then held it next to the angles, and make a mark on the paper. Then held it to the next angle and make another mark.
Now, testing sites may be different, so I can't promise you that your testing site will have the same monitoring policies as mine.
Good luck.