We are given that $\angle EHD = 106^\circ$ and we need to find $m\angle FHC$.

Looking at the diagram, we can observe the following:

• Points A, B, C, D, E, F, G, and H lie on intersecting lines.
• $\angle EHD$ and $\angle FHC$ appear to be vertically opposite angles, which means they are equal.

Thus, if $m\angle EHD = 106^\circ$, then $m\angle FHC$ must also be $106^\circ$ because vertically opposite angles are always congruent.

Final Answer:

$m\angle FHC = 106^\circ$

Let me know if you'd like further clarification or additional details!

Here are 5 related questions:

1. What are vertically opposite angles?
2. How do parallel lines influence angle relationships?
3. What is the sum of the angles in a straight line?
4. Can two obtuse angles be vertically opposite?
5. What are alternate interior angles?

Tip: Vertically opposite angles are always equal when two lines intersect!