Since triangles \( \triangle PQR \) and \( \triangle LMN \) are similar (\( \triangle PQR \sim \triangle LMN \)), their corresponding angles are equal.
First, we need to determine the measure of angle \( P \) in triangle \( PQR \):
- The sum of the angles in a triangle is \( 180^\circ \).
- Therefore, we can find \( m\angle P \): \[ m\angle P + m\angle Q + m\angle R = 180^\circ \] \[ m\angle P + 113^\circ + 26^\circ = 180^\circ \] \[ m\angle P + 139^\circ = 180^\circ \] \[ m\angle P = 180^\circ - 139^\circ = 41^\circ \]
Now, since the triangles are similar, we have:
- \( m\angle P = m\angle L \)
- \( m\angle Q = m\angle M \)
- \( m\angle R = m\angle N \)
Using angle measures:
- \( m\angle L = 41^\circ \)
- \( m\angle M = 113^\circ \)
- \( m\angle N = 26^\circ \)
Thus, the measure of angle \( N \) is: \[ \boxed{26^\circ} \]
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