Question

In the diagram below, three lines intersect at N. The measure of angle GNF is 60°, and the measure of angle MNL is 47º.Find the measurement of angle HNK

Answer 1

Notice that angles GNF, GNH and HNK lay in the same straight line. Therefore,

`\angle GNF+\angle GNH+\angle HNK=180`

Now, we know that angle GNF measures 60°. This way,

`\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}`

We also know that angles GNH and MNL are vertically opposite, meaning they are the same. This way, we have that

`\angle MNL+\angle HNK=120`

We also know that angle MNL measures 47°. This way, we can clear angle HNK and now its value:

`\begin{gathered} \angle MNL+\angle HNK=120 \\ \rightarrow47+\angle HNK=120 \\ \rightarrow\angle HNK=120-47 \\ \rightarrow\angle HNK=73 \end{gathered}`

This way, we can conlcude that:

`\angle HNK=73`