In triangle \( \triangle LMN \), we know that \( \overline{LM} \cong \overline{NL} \). This tells us that triangle \( \triangle LMN \) is isosceles, with the two sides \( LM \) and \( NL \) being congruent.
Given that \( m\angle N = 44^\circ \), we can denote \( m\angle L = x \) and \( m\angle M = x \) since the angles opposite the equal sides are equal.
Using the triangle sum theorem, we know that the sum of the angles in a triangle is \( 180^\circ \):
\[ m\angle L + m\angle M + m\angle N = 180^\circ \]
Substituting the known values:
\[ x + x + 44^\circ = 180^\circ \]
This simplifies to:
\[ 2x + 44^\circ = 180^\circ \]
Next, we can subtract \( 44^\circ \) from both sides:
\[ 2x = 180^\circ - 44^\circ \] \[ 2x = 136^\circ \]
Now, divide both sides by 2:
\[ x = \frac{136^\circ}{2} = 68^\circ \]
Thus, we find:
\[ m\angle L = 68^\circ \]
Therefore, the measure of angle \( L \) is
\[ \boxed{68^\circ} \]
3 answers