Since the triangles \( \triangle PQR \) and \( \triangle LMN \) are similar (denoted as \( \triangle PQR \sim \triangle LMN \)), the corresponding angles of these triangles are equal.
The sum of the angles in a triangle is always \( 180^\circ \).
For triangle \( PQR \):
- \( m\angle Q = 113^\circ \)
- \( m\angle R = 26^\circ \)
We can find \( m\angle P \) by using the angle sum property of triangles:
\[ m\angle P + m\angle Q + m\angle R = 180^\circ \]
Substituting in the values:
\[ m\angle P + 113^\circ + 26^\circ = 180^\circ \]
Combining the known angles:
\[ m\angle P + 139^\circ = 180^\circ \]
Now, solving for \( m\angle P \):
\[ m\angle P = 180^\circ - 139^\circ = 41^\circ \]
Since the triangles are similar:
- \( m\angle P = m\angle L \)
- \( m\angle Q = m\angle M \)
- \( m\angle R = m\angle N \)
Thus:
\[ m\angle N = m\angle R = 26^\circ \]
Hence, the measure of angle \( N \) is
\[ \boxed{26^\circ} \]
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