Answer:
The phrase "complementary line" usually has to do with business.
Example: I have a complementary line of famous products that I am trying to sell to you". Mostly just used in advertising.
Most likely, you are asking what a "complementary angle" is?
Two complementary angles will always add up to 90 degrees (pi/4).
So, if 30 degrees is the starting angle, 60 degrees would be the complementary angle.