Is there any way to test a breaker?

When I had the extra line ran to the garage, I had asked for a 30 amp breaker. It was a buddy trade deal (sort of, still cost me some coin). I had never even noticed that it was a 20 amp breaker. I had two spots where the 120 outlets were run and there is one 240 outlet with a dual pole 80 amp breaker.

I had changed to old and hacked power cord out to a 6ft 12g cable thinking the cord might be the problem. It didn't help.
Without knowing the gauge of wiring installed, I think I'll try another 20amp breaker. Barring that, this is the first time I saw the 240 wiring on the motor, so that might just be step 2.