Question

→ce and →fh are parallel lines.
which angles are vertical angles?
∠hgi and ∠fgi
∠hgi and ∠cdb
∠hgi and ∠cdg
∠hgi and ∠fgd
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Explanation:

Vertical angles are pairs of opposite angles formed by intersecting lines, sharing a common vertex and being equal in measure.

1. $\angle HGI$ and $\angle FGI$ share a side and are adjacent, forming a linear pair, not vertical angles.
2. $\angle HGI$ and $\angle CDB$ are formed by a transversal and parallel lines, making them corresponding angles, not vertical angles.
3. $\angle HGI$ and $\angle CDG$ are formed by a transversal and parallel lines, making them alternate interior angles, not vertical angles.
4. $\angle HGI$ and $\angle FGD$ are opposite each other at the intersection of lines $\overleftrightarrow{FH}$ and $\overleftrightarrow{IB}$, so they are vertical angles.

Answer:

$\boldsymbol{\angle HGI}$ and $\boldsymbol{\angle FGD}$