Question

bd and eg are parallel lines. which angles are corresponding angles? ∠gfc and ∠efc ∠gfc and ∠bcf ∠gfc and ∠gfh ∠gfc and ∠dca

Explanation:

Step1: Recall the definition of corresponding angles

Corresponding angles are angles that are in the same relative position at each intersection where a straight line crosses two others.

Step2: Analyze each option

• For $\angle GFC$ and $\angle EFC$: They are adjacent angles, not corresponding angles.
• For $\angle GFC$ and $\angle BCF$: They are alternate - interior angles (if we consider the parallel lines $BD$ and $EG$ and the transversal $HG$).
• For $\angle GFC$ and $\angle GFH$: They are adjacent angles, not corresponding angles.
• For $\angle GFC$ and $\angle DCA$: Since $\overleftrightarrow{BD}\parallel\overleftrightarrow{EG}$ and $HG$ is a transversal. $\angle GFC$ and $\angle DCA$ are in the same relative position (both are on the same side of the transversal and in the "corresponding" positions relative to the parallel lines).

Answer:

$\angle GFC$ and $\angle DCA$