Answer
∠E=38$^{\circ}$
Work Step by Step
With corresponding angles indicated,
$\angle$A=57$^{\circ}$
$\angle$C=85$^{\circ}$
$\angle$B=?$^{\circ}$
as per rules and formula the sum of all the angles of triangle is always equal to 180$^{\circ}$
therefore,
$\angle$A+$\angle$B+$\angle$C=180$^{\circ}$
57$^{\circ}$+$\angle$B+85$^{\circ}$=180$^{\circ}$
$\angle$B=180$^{\circ}$-142$^{\circ}$
∠B=38$^{\circ}$
and here
$\angle$A=$\angle$F
$\angle$C=$\angle$D
$\angle$B=$\angle$E
