To solve the problem depicted in the image, we need to determine the measure of certain angles in the given geometric configuration.

Given:

• $m \angle 7 = 125^\circ$
• $m \angle 13 = 50^\circ$

The diagram appears to be a combination of intersecting lines and possibly a triangle with extended sides, where some angles are indicated by their measures.

Approach:

1. Identify relationships between angles:

   • Vertical angles (opposite angles formed by intersecting lines) are equal.
   • Linear pairs of angles (adjacent angles formed by intersecting lines) sum to $180^\circ$.
   • Angles on a straight line also sum to $180^\circ$.

2. Analyze the given information:

   • $m \angle 7$ and $m \angle 8$ form a linear pair. Thus, $m \angle 8 = 180^\circ - 125^\circ = 55^\circ$.
   • $m \angle 13$ is given as $50^\circ$.

3. Use the triangle's angle sum property:

   • The sum of the interior angles of any triangle is $180^\circ$.

Solution:

To fully determine the unknown angles, the exact positions of angles $m \angle 7$ and $m \angle 13$ need to be identified relative to the other angles. If they belong to different sections of the diagram, the relationships between these sections need to be clarified.

Given the information and typical properties of intersecting lines and triangles, further steps can be taken, but this depends on the context and the other angles not shown directly in the image.

Would you like more detailed analysis, or do you have any specific questions about this problem? Here are five questions that could further explore this topic:

1. How do vertical angles help determine unknown angles in intersecting lines?
2. What is the significance of a linear pair of angles?
3. How can the angle sum property of a triangle be applied in complex figures?
4. How do you identify corresponding angles when dealing with parallel lines and transversals?
5. What are supplementary angles, and how are they used in solving angle problems?

Tip: When solving geometric problems involving angles, always start by identifying known relationships, like linear pairs or vertical angles, to gradually uncover unknown measures.