What a big difference a small change can make

Geometry Level 5

I have three analog clocks. Clock 1 is correct, Clock 2 gains one minute every hour, and Clock 3 loses one minute every hour. I set them all to the correct time at \(12\) AM. At \(8 \! : \! 20\) PM, the angle between the hour and minute hands on Clock 1 is \(A^{\circ}\), the angle between the hour and minute hands on Clock 2 is \(B^{\circ}\), and the angle between the hour and minute hands on Clock 3 is \(C^{\circ}\). Assume \(0 \leq A, B, C \leq 180\). Find the value of \(\left \lfloor A + B + C \right \rfloor\).

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