Angles of Orthic Triangle of Acute Triangle/Proof

Proof

 * Orthic-Triangle.png

Let $H$ be the orthocenter of $\triangle ABC$.

The quadrilateral $\Box FHDB$ is cyclic.

That is, $\Box FHDB$ can be circumscribed.

Hence:

Similarly, $\Box DHEC$ is also a cyclic quadrilateral.

Then:

The same argument can be applied to $B$ and $C$.

Hence the result.