Question

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

Explanation:

Step1: Recall definition

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

Step2: Analyze each option

For $\angle BCF$ and $\angle EFC$, they are on the same - side of transversal $EF$ and between lines $AB$ and $EG$.
For $\angle EFC$ and $\angle EFH$, they are adjacent angles, not consecutive - interior angles.
For $\angle GFC$ and $\angle DCA$, they are not between the relevant lines.
For $\angle DCF$ and $\angle BCA$, they are vertical angles, not consecutive - interior angles.

Answer:

$\angle BCF$ and $\angle EFC$