What are the angles used in angle connectors and liftarms?
The regular connector have simple angles which are multiples of 22.5°. #4 is 45°, #3 is 22.5° and #5 is 67.5°. That's pretty boring stuff, but there you go.

The 53.5 angle isn't as bizarre as you would think and there's a very good reason for it (and less boring to me, but YMMV).

That reason is that it forms a Pythagorean triangle, and specifically the best known 3:4:5 one, meaning these liftarms can be used together with regular right-angle frames to make sturdy constructions.

The one you chose isn't the best example as the beam doesn't extend to the full  hypotenuse (the connection points need to be 5 studs apart), but the longer one is perfect for that. If the small side is attached to a beam, the cross at the end of the long side will be perfectly aligned on a beam that would be 4 studs higher.

LEGO uses that to connect beams 4 studs apart in a very solid way, for example in 8435 - 4WD (the blue beam behind the front wheel) or in the more recent 8053 - Mobile Crane (left of the linear actuator)

And for the record, the angle in degrees is weirder that just 53.5°; it's actually 53.130102...°, or the invert cosine of 3/5. So if you thought Pythagoras and trigonometry wouldn't come and annoy you in your play, you're oh so wrong.