Given the following:
[tex]\measuredangle LKM\cong\measuredangle JKN[/tex]
for angles JKM and LKN, we can use the angle addition postulate to get the following:
[tex]\begin{gathered} \measuredangle JKM=\measuredangle JKN+\measuredangle NKM \\ \measuredangle LKN=\measuredangle LKM+\measuredangle NKM \end{gathered}[/tex]
but angles LKM and JKN are congruent, therefore:
[tex]\begin{gathered} \measuredangle JKM=\measuredangle JKN+\measuredangle NKM=\measuredangle LKN \\ \Rightarrow\measuredangle JKM=\measuredangle LKN \end{gathered}[/tex]
