Perhaps he's talking about phase angle control in SCR light dimmers and the like.
If so, I guess the firing angle would refer to the number of degrees at which the SCR "fires" (is triggered), relative to the start of the half-cycle, and the conduction angle would refer to the total angle for which the SCR conducts.
In that case, firing angle + conduction angle = 180 degrees (roughly - because the SCR will drop out slightly before the end of the half-cycle due to insufficient holding curent).
https://en.wikipedia.org/wiki/Phase_angle_control