Given:
The lines l and m are parallel lines and x=40 degrees.
To find the angle:
[tex]\angle\text{DEF}[/tex]We know that alternate angles are equal.
So that,
[tex]\begin{gathered} \angle EDG=x \\ =40^{\circ} \end{gathered}[/tex]And then, using the angle sum property of a triangle,
[tex]\begin{gathered} \angle EDG+\angle DFE+\angle DEF=180^{\circ} \\ 40^{\circ}+40^{\circ}+\angle DEF=180^{\circ} \\ \angle DEF=180^{\circ}-40^{\circ}-40^{\circ} \\ \angle DEF=100^{\circ} \end{gathered}[/tex]Thus, the measure of angle DEF is 100 degrees.