On a protractor, ray $BA$ goes through the 85-degree mark and ray $BC$ goes through the 30-degree mark. What is the measure, in degrees, of angle $ABC$?

[asy]
draw((0,0)--(2,0)..(1,1)..(0,0)..cycle,linewidth(2));

draw((1,0)--1.4dir(30)+(1,0),Arrow);
draw((1,0)--1.3dir(85)+(1,0),Arrow);

dot(1.1dir(85)+(1,0));
dot(1.2dir(30)+(1,0));

label("A",1.1dir(85)+(1,0),NW);
label("B",(1,0),S);
label("C",1.2dir(30)+(1,0),SE);

label("85",.9dir(85)+(1,0));
label("30",.9dir(30)+(1,0));

[/asy]
The measure of angle $ABC$ is $85-30=\boxed{55}$ degrees.