Actually guys, 36 teeth is not 36 teeth in terms of degrees. If any of you have ever worked on various engines you would know that a 60 tooth trigger wheel is not always 6 degrees between teeth. Believe or not, a "tooth" is not a ISO standard item. There are different pitches, different tooth profiles, different flats on the teeth, different valleys on the teeth. On some 60-2 trigger wheels I have ~2 - 3 degrees of "rise" on a crankshaft signal sensor before seeing the flat and have the same "fall" before seeing the valley. Other trigger wheels, also 60-2, have square teeth with hard edges and thus an event is triggered merely by the presence of the tooth or not - there is no rise or fall. Much the same on a ratchet, there is surely different ramp rates between teeth, different flat lengths, if flats at all, etc.
Further, you have spring and pawl tooth depth/ramp/flat/width as well. If a the pawl is deep then it will have higher degree of backlash before engaging the main gear.
Yes, a 36 tooth gear will have the same degrees between [measuring point]. No one is arguing that one circle has more than 360 degrees compared to the next. The point is, geometrically, the "teeth" do not have to be, and rarely are, the same shape. If a gear was a gear was a gear... we wouldn't have drawings like this:
And thus, the only way to truly measure degree of engagement is to use an angle gauge. Between the gear pitch/spacing/shape as well as backlash in the pawl and mechanics therein, you can say "a 36 tooth ratchet has 10 deg of engagement" but I bet you would actually be closer to 12 - 15 degrees once everything lines up.