1. The problem asks to find the measure of angle $\angle LMN$ formed by two intersecting lines at vertex $M$. 2. To find the measure of an angle formed by two lines, we typically use geometric properties or given measurements. 3. Since the image shows one line horizontal and the other line extending upward from the vertex, the angle $\angle LMN$ is the angle between the horizontal line and the upward line. 4. If the upward line is perpendicular to the horizontal line, then $\angle LMN = 90^\circ$. 5. Without additional measurements or information, the most common interpretation is that the angle formed is a right angle. 6. Therefore, the measure of $\angle LMN$ is $90^\circ$. Final answer: $\boxed{90^\circ}$