Question

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

Explanation:

Step1: Recall alternate exterior angles definition

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

Step2: Analyze each option

• For $\angle DCA$ and $\angle EFH$:
• Lines $\overleftrightarrow{BD}$ and $\overleftrightarrow{EG}$ are parallel, and $\overleftrightarrow{AH}$ is the transversal.
• $\angle DCA$ lies outside $\overleftrightarrow{BD}$, $\angle EFH$ lies outside $\overleftrightarrow{EG}$, and they are on opposite sides of transversal $\overleftrightarrow{AH}$.
• For $\angle BCA$ and $\angle BCF$: These are adjacent angles (share a common side $BC$), not alternate exterior angles.
• For $\angle EFC$ and $\angle GFH$: These are adjacent angles (share a common side $FH$), not alternate exterior angles.
• For $\angle BCF$ and $\angle GFC$: These are adjacent angles (share a common side $CF$), not alternate exterior angles.

Answer:

$\angle DCA$ and $\angle EFH$