Question

which angles are vertical angles? \
(image of lines and angles with points i, f, e, g, h, k, j, l) \
options: \
$\angle hgj$ and $\angle kjl$ \
$\angle fgj$ and $\angle kjl$ \
$\angle hge$ and $\angle fgj$ \
$\angle fgj$ and $\angle ijg$

Explanation:

Step1: Recall vertical angles definition

Vertical angles are opposite angles formed by two intersecting lines, and they are equal in measure.

Step2: Analyze each option

• Option 1: $\angle HGJ$ and $\angle KJL$: These angles are not formed by the same intersecting lines, so not vertical angles.
• Option 2: $\angle FGJ$ and $\angle KJL$: These angles are not opposite angles from intersecting lines, so not vertical angles.
• Option 3: $\angle HGE$ and $\angle FGJ$: $\angle HGE$ and $\angle FGJ$ are opposite angles formed by the intersection of lines $LE$ and $FH$, so they are vertical angles.
• Option 4: $\angle FGJ$ and $\angle IJG$: These angles are not opposite angles from intersecting lines, so not vertical angles.

Answer:

$\angle HGE$ and $\angle FGJ$ (the option with $\angle HGE$ and $\angle FGJ$)