On the diagram in the book JKMN looks like a square, but from the information given in the text this cannot be true. Let's draw a slightly different diagram highlighting the information given.
We are asked to compare two angles of triangle KLN.
We can do this by comparing the opposite two sides first.
To compare these segments, let's focus on triangles △ LJN and △ LJK.
Now we will summarize what we know about these triangles.
Claim
Justification
KJ≅JN
Given in the question.
m∠ LJN> m∠ KJL
Given in the question.
Since JL is a common side of triangles △ LJN and △ LJK, these triangles have two pairs of congruent sides.
This means that we can use the Hinge Theorem.
m∠ LJN> m∠ KJL
⇓
NL> KL
We can now turn our attention back to triangle KLN.
Since we now know the relationship between two of the sides, we can use the Angle-Side Relationships to compare the opposite angles.
NL> KL
⇓
m∠ LKN> m∠ LNK
