Question

\overrightarrow{df} and \overrightarrow{gi} are parallel lines.

which angles are vertical angles?

\angle deh and \angle fec
\angle deh and \angle ihj
\angle deh and \angle dec
\angle deh and \angle feh

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines. They are opposite each other and have equal measures.

Step2: Analyze each option

• For $\angle DEH$ and $\angle FEC$:

These two angles are formed by the intersection of lines $JC$ and $DF$ (since $DF$ and $GI$ are parallel, but the key is the intersection of $JC$ and $DF$ at point $E$). They are non - adjacent and opposite each other.

• For $\angle DEH$ and $\angle IHJ$:

These angles are not formed by the intersection of the same two lines. $\angle DEH$ is formed by the intersection of $JC$ and $DF$, while $\angle IHJ$ is formed by the intersection of $JC$ and $GI$.

• For $\angle DEH$ and $\angle DEC$:

These two angles are adjacent, not vertical.

• For $\angle DEH$ and $\angle FEH$:

These two angles are adjacent (they share a common side $EH$), not vertical.

Answer:

$\angle DEH$ and $\angle FEC$