"Angles and Dangles" is a term used by submariners for the critical manuevers that usually takes place soon after the nuclear submarine has left port. Once the sub has reached deep water, the sub is put through "angles" or alternating deep, steep dives and steep climb outs. During "angles" anything that is not properly secured will shake, rattle, fall, etc. and make some sort of noise. These items which shake loose are known as "dangles", and they must be corrected before the sub is fully considered as silent running. Basically, the sub dives deep and comes up steep repeatedly while listening for any sounds.
After the sub was put through angles and dangles many items were found to improperly secured, because many sounds were detected.