Question

which angles are consecutive interior angles? ∠bcf and ∠efc ∠dcf and ∠gfh ∠bca and ∠gfh ∠gfh and ∠dca

Explanation:

Step1: Recall definition of consecutive - interior angles

Consecutive - interior angles are two angles that lie between two lines and on the same side of a transversal.

Step2: Analyze each option

For $\angle BCF$ and $\angle EFC$, they lie between lines $AB$ and $EG$ and on the same side of transversal $HF$.
For $\angle DCF$ and $\angle GFH$, $\angle DCF$ is formed by $AB$ and $HF$, $\angle GFH$ is formed by $EG$ and $HF$, but they are not in the correct position relationship of consecutive - interior angles.
For $\angle BCA$ and $\angle GFH$, they are not in the position of consecutive - interior angles.
For $\angle GFH$ and $\angle DCA$, they are not in the position of consecutive - interior angles.

Answer:

$\angle BCF$ and $\angle EFC$