If E,F,G is the altitude of triangle and D is on EF does that mean angle ADC=90?

Question

Let $ABC$ be an acute triangle and $E, F, G$ be an altitude of triangle on $AB, BC, AC$ respectively and $EF$ intersect $BG$ at $D$.

I don't know whenever $\angle{ADC}$ is really 90° or not but it looks like it is really 90°. If it is really 90° then it'd great ( I need this to solve other problem ). Please help

Answer 1

In this image, it is $105.5+^\circ$, and I didn't even search for a non-example.