Question

select all the pairs of vertical angles.
∠gfh and ∠bca ∠dca and ∠efc
∠gfc and ∠efh ∠dca and ∠bcf

Explanation:

Step1: Recall vertical angles definition

Vertical angles are opposite angles formed by two intersecting lines, and they are equal.

Step2: Analyze each option

• For $\angle GFH$ and $\angle BCA$: These angles are not formed by the same intersecting lines, so not vertical angles.
• For $\angle DCA$ and $\angle EFC$: These angles are not opposite angles from intersecting lines, so not vertical angles.
• For $\angle GFC$ and $\angle EFH$: Lines $EG$ and $AH$ intersect at $F$, so $\angle GFC$ and $\angle EFH$ are opposite angles (vertical angles).
• For $\angle DCA$ and $\angle BCF$: Lines $BD$ and $AH$ intersect at $C$, so $\angle DCA$ and $\angle BCF$ are opposite angles (vertical angles).

Answer:

$\angle GFC$ and $\angle EFH$, $\angle DCA$ and $\angle BCF$