The greater the angle the greater side length theorem indicates that the order of the side lengths from least to greatest is; IJ < LK < IL < JL < IK
The steps used to find the order of the side lengths of the triangles from the least to greatest is presented as follows;
The measure of the angle ∠ILJ in triangle ΔIJL is; 180 - (55 + 81) = 44°
The measure of angle ∠ILK is; 180 - 44 = 136°
The measure of the angle ∠LIK is; 180 - (136 + 16) = 28°
The triangle greater angle greater side theorem indicates that we get;
m∠JIK is; 55 + 28 = 83°
Therefore in triangle ΔJIK, IJ < IK < JK
The angle side length theorem applied to triangle ΔJIL indicates;
IJ < JL < IL
The angle side length theorem applied to triangle ΔLIK indicates;
IL < LK < IK
Therefore; IJ < LK <
IJ < LK < IL < JL < IK