Since triangles \( \triangle PQR \) and \( \triangle LMN \) are similar (denoted as \( \triangle PQR \sim \triangle LMN \)), the corresponding angles are equal.
Given:
- \( m\angle Q = 113^\circ \)
- \( m\angle R = 26^\circ \)
To find the measure of angle \( P \) in triangle \( PQR \), we use the fact that the sum of the interior angles of a triangle is \( 180^\circ \).
\[ m\angle P + m\angle Q + m\angle R = 180^\circ \] \[ m\angle P + 113^\circ + 26^\circ = 180^\circ \] \[ m\angle P + 139^\circ = 180^\circ \] \[ m\angle P = 180^\circ - 139^\circ = 41^\circ \]
Now, since \( \triangle PQR \sim \triangle LMN \), we know:
- \( m\angle L = m\angle P = 41^\circ \)
- \( m\angle M = m\angle Q = 113^\circ \)
- \( m\angle N = m\angle R = 26^\circ \)
Thus, the measure of angle \( N \) is: \[ \boxed{26^\circ} \]
2 answers