in a triangle, all the angles add up to 180 degrees. so if angle B = 120, then angle A + angle C = 180 - 120 = 60.

so if angle A is 60, it would mean angle C is 0, and so we would not have a triangle. thus angle A must be less than 60 which means angle A is not equal to 60 degrees

you can fix this up this proof if you want