Question

If ADEF ALJK, what is the m4D?KDV12mz D=42Ftype your answer...301.

Answer 1

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:

$m\angle D=57^{\circ}.$