Question

df and gt are parallel lines. which angles are vertical angles? ∠deh and ∠ghe ∠deh and ∠fec ∠deh and ∠dec ∠deh and ∠feh

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are opposite angles formed by two intersecting lines.

Step2: Analyze each option

• For $\angle DEH$ and $\angle GHE$: These are not vertical angles. They are alternate - interior angles (since $DF\parallel GI$ and $CJ$ is a transversal).
• For $\angle DEH$ and $\angle FEC$: Lines $DF$ and $CJ$ intersect at point $E$. $\angle DEH$ and $\angle FEC$ are opposite angles formed by the intersection of these two lines. So, they are vertical angles.
• For $\angle DEH$ and $\angle DEC$: These two angles are adjacent angles (they share a common side $EC$ and a common vertex $E$).
• For $\angle DEH$ and $\angle FEH$: These two angles are adjacent angles (they share a common side $EH$ and a common vertex $E$) and they are supplementary ($\angle DEH+\angle FEH = 180^{\circ}$ as they form a linear pair).

Answer:

$\angle DEH$ and $\angle FEC$