Notice that angles GNF, GNH and HNK lay in the same straight line. Therefore,
[tex]\angle GNF+\angle GNH+\angle HNK=180[/tex]
Now, we know that angle GNF measures 60°. This way,
[tex]\begin{gathered} \angle GNF+\angle GNH+\angle HNK=180 \\ \rightarrow60+\angle GNH+\angle HNK=180 \\ \rightarrow\angle GNH+\angle HNK=180-60 \\ \rightarrow\angle GNH+\angle HNK=120 \end{gathered}[/tex]
We also know that angles GNH and MNL are vertically opposite, meaning they are the same. This way, we have that
[tex]\angle MNL+\angle HNK=120[/tex]
We also know that angle MNL measures 47°. This way, we can clear angle HNK and now its value:
[tex]\begin{gathered} \angle MNL+\angle HNK=120 \\ \rightarrow47+\angle HNK=120 \\ \rightarrow\angle HNK=120-47 \\ \rightarrow\angle HNK=73 \end{gathered}[/tex]
This way, we can conlcude that:
[tex]\angle HNK=73[/tex]
