To solve for $m \angle ?$, we need to use geometric relationships, particularly focusing on triangle angle sum properties and linear pairs of angles.

Step-by-Step Solution:

1. The sum of angles in a triangle is always $180^\circ$. Therefore, we can use this property for the two visible triangles.

Left Triangle:

• The angles are $37^\circ$, $85^\circ$, and the third unknown angle (let's call it $x$).
• The sum of angles in this triangle is $180^\circ$, so: $37^\circ + 85^\circ + x = 180^\circ$ Solving for $x$: $x = 180^\circ - (37^\circ + 85^\circ) = 180^\circ - 122^\circ = 58^\circ$

Right Triangle:

• The angles are $52^\circ$, $62^\circ$, and the unknown angle (let's call it $y$).
• The sum of angles in this triangle is $180^\circ$, so: $52^\circ + 62^\circ + y = 180^\circ$ Solving for $y$: $y = 180^\circ - (52^\circ + 62^\circ) = 180^\circ - 114^\circ = 66^\circ$

Solving for $m \angle ?$:

• The angle labeled $?$ forms a vertical pair with $x = 58^\circ$ (from the left triangle).
• Vertical angles are congruent, so: $m \angle ? = 58^\circ$

Thus, the measure of $\angle ?$ is $\boxed{58^\circ}$.

Would you like more details or clarification on any step?

Here are some related questions you could explore:

1. How do vertical angles help in solving geometric problems?
2. What is the angle sum property of a triangle, and how is it applied?
3. How do we find angles in polygons other than triangles?
4. How can supplementary angles help in geometry problems?
5. Can this problem be solved using alternate methods such as parallel line angles?

Tip: Always remember that the sum of angles in any triangle is $180^\circ$, which is key to solving many geometry problems.