Step 1: Proteins absorb UV light mainly because of their aromatic amino acids, tryptophan, tyrosine and phenylalanine, which absorb in the 250-290 nm range with a peak near 280 nm.
Step 2: Among the three, tryptophan is by far the strongest absorber. It absorbs UV roughly ten times more efficiently than phenylalanine or tyrosine, so it makes the largest single contribution to a protein's absorbance at 280 nm.
Step 3: Adding tryptophan therefore raises UV absorption the most. Leucine, proline and arginine are not aromatic and do not absorb appreciably in this region.
This is why A280 readings are used to estimate protein concentration.
Ref: Rebecca James, Self Assessment and Review of Biochemistry, 3rd edn, pg 7.