I think this game would be better if you had a finite amount of angles to guess, rather than an unbounded amount and a time limit. Maybe put a time limit on each individual one, but just so people don't have time to grab a protractor.
As it is, speed is rewarded more than accuracy.
Also, I lost a bit of time before I realised that "6" wasn't an acceptable answer, but "6.0" was.
Also also, I think the marking logic for small angles is a bit mean.
0.3 - 5 ticks
0.2 - 0 ticks
I'd make the score based on absolute difference rather than percentage difference, or perhaps a mix of the two somehow.
Why did the vector cross the road?
It wanted to be normal.
Wow ... in depth review!
I can tackle the last one first: I will make the scoring to be "lose 1 star per 0.08 radians wrong" so 0.6 instead of 0.5 gets 4 stars.
Also maybe a small explanation at top "answer like 0.6, 2.0 etc" ?
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman