Question

which angles are corresponding angles? ∠bca and ∠efc ∠bca and ∠gfc ∠bca and ∠bcf ∠bca and ∠dcf

Explanation:

Step1: Recall corresponding - angles definition

Corresponding angles are in the same relative position at each intersection where a straight - line crosses two others. If the two lines are parallel, corresponding angles are equal.

Step2: Analyze each option

• For $\angle BCA$ and $\angle EFC$: They are in the same relative position with respect to the transversal $AC$ and the two lines $EG$ and $BD$. When a transversal intersects two lines, these angles are corresponding angles.
• $\angle BCA$ and $\angle GFC$: $\angle GFC$ is not in the corresponding - angle position with $\angle BCA$.
• $\angle BCA$ and $\angle BCF$: These are adjacent angles, not corresponding angles.
• $\angle BCA$ and $\angle DCF$: These are vertical angles, not corresponding angles.

Answer:

$\angle BCA$ and $\angle EFC$