Question

these figures are congruent. what is ( mangle j )?

Explanation:

Step1: Find $\angle F$ in $\triangle EFD$

The sum of angles in a triangle is $180^\circ$.
$m\angle F = 180^\circ - 44^\circ - 59^\circ = 77^\circ$

Step2: Match congruent angles

Congruent triangles have matching angles. $\angle J$ corresponds to $\angle D$? No, match sides/angles: $\angle D = 59^\circ$, $\angle K = 59^\circ$, so $\angle J$ matches $\angle F$? No, correct match: $\triangle JKL$ has $\angle K=59^\circ$, $\angle L=77^\circ$, so $\angle J = 180 - 59 -77 = 44^\circ$. Alternatively, congruent to $\angle E=44^\circ$.
$m\angle J = 44^\circ$

Answer:

$44^\circ$