Question

which angles are alternate interior angles? image of lines and angles ∠efc and ∠gfh; ∠efc and ∠dcf; ∠efc and ∠bca; ∠efc and ∠dca

Explanation:

Step1: Recall Alternate Interior Angles Definition

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two lines (interior) and on opposite sides of the transversal.

Step2: Analyze Each Option

• Option 1: ∠EFC and ∠GFH

These are vertical angles (opposite angles formed by intersecting lines), not alternate interior angles.

• Option 2: ∠EFC and ∠DCF

Lines \( BD \) and \( EG \) are parallel (implied by the diagram’s structure), and transversal \( AH \) crosses them. \( ∠EFC \) and \( ∠DCF \) lie between \( BD \) and \( EG \) (interior) and on opposite sides of \( AH \) (transversal). This matches the alternate interior angles definition.

• Option 3: ∠EFC and ∠BCA

\( ∠BCA \) is not in the interior region between the two parallel lines relative to \( ∠EFC \), so this is incorrect.

• Option 4: ∠EFC and ∠DCA

\( ∠DCA \) is above line \( BD \), outside the interior region between \( BD \) and \( EG \), so this is incorrect.

Answer:

∠EFC and ∠DCF (the second option)