To solve for $m\angle ABC$, let's analyze the given information.

Given:

• $m\angle ABD = 110^\circ$
• $m\angle DBC = 35^\circ$
• We need to find $m\angle ABC$.

Step-by-step solution:

1. Identify the relevant angles:

   • $\angle ABC$ is the sum of two smaller angles:
     $m\angle ABC = m\angle ABD + m\angle DBC$

2. Apply the given values: $m\angle ABC = 110^\circ + 35^\circ$

3. Calculate: $m\angle ABC = 145^\circ$

Final Answer:

$m\angle ABC = 145^\circ$

Would you like further clarification or an explanation of any steps?

Here are some related questions for deeper understanding:

1. What is the concept of adjacent angles?
2. How can we use angle addition in polygons?
3. Are there any angle properties related to triangles that might change if the lines intersect differently?
4. How do linear pairs and supplementary angles differ from adjacent angles?
5. What are some practical applications of these angle addition properties?

Tip: When adding angles, always ensure the angles are correctly aligned with the points involved (like $A, B, D, C$ here) to avoid confusion!