Question

select all the pairs of vertical angles.
∠hge and ∠fgj
∠ij g and ∠kjl
∠hgj and ∠fge
∠kjg and ∠hgj

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are formed when two lines intersect. They are opposite each other and are congruent.

Step2: Analyze intersections

At the intersection of lines $EH$ and $FK$ at point $G$, $\angle HGE$ and $\angle FGJ$ are vertical angles, and $\angle HGJ$ and $\angle FGE$ are vertical angles.

Step3: Analyze other intersections

At the intersection of lines $EH$ and $IK$ at point $J$, $\angle IJG$ and $\angle KJL$ are vertical angles. Since $\angle KJG$ and $\angle HGJ$ are not formed by the same intersection of two lines, they are not vertical angles.

Answer:

$\angle HGE$ and $\angle FGJ$, $\angle IJG$ and $\angle KJL$, $\angle HGJ$ and $\angle FGE$