Question

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

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 the lines \(EG\) and \(BD\) with transversal \(AH\):

• \(\angle DCF\) and \(\angle GFC\) lie between \(EG\) and \(BD\) and on the same side of \(AH\).
• \(\angle BCA\) and \(\angle EFC\): \(\angle BCA\) and \(\angle EFC\) are not consecutive - interior angles as they are not in the correct position relationship.
• \(\angle EFC\) and \(\angle DCA\): They are not consecutive - interior angles.
• \(\angle EFH\) and \(\angle GFC\): \(\angle EFH\) and \(\angle GFC\) are vertical angles, not consecutive - interior angles.

Answer:

\(\angle DCF\) and \(\angle GFC\)