Let's solve the problem.

We are given:

• $m\angle ABC = 110^\circ$
• $m\angle 2 = 36^\circ$

We need to find $m\angle ABD$.

Step-by-step solution:

1. $\angle ABC$ is the entire angle from ray $AB$ to ray $BC$.

2. $\angle ABD$ and $\angle 2$ (which is $\angle DBC$) are adjacent angles that together form $\angle ABC$. Hence, their measures add up to the total measure of $\angle ABC$: $m\angle ABC = m\angle ABD + m\angle 2$ Substituting the known values: $110^\circ = m\angle ABD + 36^\circ$

3. Solve for $m\angle ABD$: $m\angle ABD = 110^\circ - 36^\circ = 74^\circ$

Final Answer:

$m\angle ABD = 74^\circ$

Would you like me to explain any steps in more detail or provide additional examples?

Here are five follow-up questions to deepen understanding:

1. What are adjacent angles, and how do they relate to this problem?
2. How can you determine if two angles are complementary or supplementary?
3. If another angle, $\angle EBD$, were added, how would you find its measure?
4. Can angles in the same configuration sum to more than $180^\circ$? Why or why not?
5. How do you distinguish between interior and exterior angles?

Tip: Always double-check angle relations (like adjacent or supplementary) to ensure your equations are correct!