Given that:
[tex]\Delta DEF\cong\Delta LJK,[/tex]
we get that:
[tex]\begin{gathered} m\angle D=m\angle L, \\ m\angle E=m\angle J, \\ m\angle F=m\angle K. \end{gathered}[/tex]
Now, recall that the interior angles of a triangle add up to 180°, therefore:
[tex]\begin{gathered} m\angle D+m\angle E+m\angle F=180^{\circ}, \\ m\angle D=180^{\circ}-m\angle E-m\angle F. \end{gathered}[/tex]
Substituting:
[tex]\begin{gathered} m\angle F=42^{\circ}, \\ m\angle E=m\angle J=81^{\circ}, \end{gathered}[/tex]
in the previous equation, we get:
[tex]m\angle D=180^{\circ}-42^{\circ}-81^{\circ}=57^{\circ}.[/tex]
Answer:
[tex]m\angle D=57^{\circ}.[/tex]
