I don't remember seeing an "m" before . My guess would be that it stands for "measure", i.e., the magnitude of the angle as opposed to the angle itself as a geometric figure.
Ok one confusion remains ,i have noticed that m symol is everywhere in the statements , but the author put it where there is equal sign(=) like sum of angles e.g m<ABC + m<BCD=90 here is m , where there is congruency of anlges there is no 'm' sign e.g <ABC=~ <BCD (=~ is for congrueny ) :-) so now could please define y is 'm' sign here ?
To add, when we take a sum of two angles, we must use to convert angles as figures to numbers first and then to add the results. That's why is used in . To say that two angles are congruent, we don't need since we could say . The latter fact is equivalent to .