Question

bd and eg are parallel lines. which angles are alternate exterior angles? ∠bcf and ∠gfh ∠gfh and ∠bca ∠bcf and ∠bca ∠efc and ∠bcf

Explanation:

Step1: Recall the definition of alternate exterior angles

Alternate exterior angles are non - adjacent angles that lie outside the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each option

• For \(\angle BCF\) and \(\angle GFH\):

Since \(\overleftrightarrow{BD}\parallel\overleftrightarrow{EG}\) and \(\overleftrightarrow{AH}\) is the transversal. \(\angle BCF\) and \(\angle GFH\) are non - adjacent, lie outside the parallel lines \(\overleftrightarrow{BD}\) and \(\overleftrightarrow{EG}\), and on opposite sides of the transversal \(\overleftrightarrow{AH}\).

• For \(\angle GFH\) and \(\angle BCA\): \(\angle GFH\) and \(\angle BCA\) do not satisfy the position relationship of alternate exterior angles.
• For \(\angle BCF\) and \(\angle BCA\): These two angles are adjacent, so they are not alternate exterior angles.
• For \(\angle EFC\) and \(\angle BCF\): These two angles are adjacent (they form a linear pair), so they are not alternate exterior angles.

Answer:

\(\angle BCF\) and \(\angle GFH\)