1 Answer

Manuel Di Iorio · Answer 1 · 2023-05-11T09:05:41+0000

Given that:

$\Delta DEF\cong\Delta LJK,$

we get that:

$\begin{gathered} m\angle D=m\angle L, \\ m\angle E=m\angle J, \\ m\angle F=m\angle K. \end{gathered}$

Now, recall that the interior angles of a triangle add up to 180°, therefore:

$\begin{gathered} m\angle D+m\angle E+m\angle F=180^(\circ), \\ m\angle D=180^(\circ)-m\angle E-m\angle F. \end{gathered}$

Substituting:

$\begin{gathered} m\angle F=42^(\circ), \\ m\angle E=m\angle J=81^(\circ), \end{gathered}$

in the previous equation, we get:

$m\angle D=180^(\circ)-42^(\circ)-81^(\circ)=57^(\circ).$

Answer:

$m\angle D=57^(\circ).$