In order to determine angle ECF we need first to determine angle ACG to do that we will use triangle GCA, since the sum of the interior angles must be 180 degrees, that is:
[tex]\angle AGC+\angle GCA+\angle CAG=180[/tex]
Replacing the known angles:
[tex]90+\angle GCA+53=180[/tex]
Adding like terms:
[tex]143+\angle GCA=180[/tex]
Subtracting 143 to both sides:
[tex]\begin{gathered} \angle GCA=180-143 \\ \angle GCA=37 \end{gathered}[/tex]
Since angle GCA equals angle ECF we have:
[tex]\angle ECF=37[/tex]
