Since triangle PQR is similar to triangle LMN (denoted as triangle PQR ~ triangle LMN), their corresponding angles are equal.
In triangle PQR, the measures of angles Q and R are given as follows:
- m∠Q = 113 degrees
- m∠R = 26 degrees
To find the measure of angle P in triangle PQR, we can use the fact that the sum of angles in a triangle is 180 degrees:
\[ m∠P + m∠Q + m∠R = 180 \]
Substituting the measures of angles Q and R into the equation:
\[ m∠P + 113 + 26 = 180 \]
Now, simplifying:
\[ m∠P + 139 = 180 \] \[ m∠P = 180 - 139 = 41 \text{ degrees} \]
Now that we have m∠P, we can determine the corresponding angle m∠L in triangle LMN, which is equal to m∠P:
\[ m∠L = m∠P = 41 \text{ degrees} \]
Next, we can find m∠N in triangle LMN using the same principle that the sum of the angles in triangle LMN is also 180 degrees:
\[ m∠L + m∠M + m∠N = 180 \]
From the similarity of the triangles, we know:
- m∠M corresponds to m∠Q, so \(m∠M = 113\) degrees.
- m∠L we found to be 41 degrees.
Now we can substitute these values into the equation:
\[ 41 + 113 + m∠N = 180 \]
Simplifying:
\[ 154 + m∠N = 180 \]
Now, solve for m∠N:
\[ m∠N = 180 - 154 = 26 \text{ degrees} \]
Therefore, the measure of angle N is \( \boxed{26} \) degrees.