Which angle is vertical to <HGJ?

<DGF
<DGE
<EHG
<FDG

no -- it must have G as the vertex. So, I'd pick <DGE

Apologies for the confusion. You are correct. <DGE is the angle that is vertical to <HGJ.

The angle that is vertical to <HGJ is <FDG.

<EHG