Luke subtracted 128° from 180° and found that the measurement of ∠str is 52°. how can luke use this information to find the measurement of ∠rst? what is the measurement of ∠rst?

STR is a triangle as shown in the picture. If Luke decided to subtract 128º from 180º, that's because he understood that the sum of the internal angles in a triangle is 180º, and therefore the angles RST and TRS together make 128º.
As a result, RST will be
128º - TRS
where TRS is the angle at R, as shown in the picture