Let's break down the information from the problem and solve for $m \angle EBD$:

Given Information:

1. $m \angle ABD = 100^\circ$
2. Line $BC$ bisects $\angle ABD$, meaning $m \angle ABC = m \angle CBD$.
3. Line $BE$ bisects $\angle CBD$, meaning $m \angle CBE = m \angle EBD$.

Step-by-step Solution:

1. Since $BC$ bisects $\angle ABD$, we know that: $m \angle ABC = m \angle CBD = \frac{m \angle ABD}{2} = \frac{100^\circ}{2} = 50^\circ$

2. Now, since $BE$ bisects $\angle CBD$, we know that: $m \angle CBE = m \angle EBD = \frac{m \angle CBD}{2} = \frac{50^\circ}{2} = 25^\circ$

Thus, $m \angle EBD = 25^\circ$.

Final Answer:

$m \angle EBD = 25^\circ$

Would you like further details on this solution or have any additional questions?

Here are 5 related questions to expand your understanding:

1. How do you calculate an angle bisector in a triangle?
2. What is the significance of an angle bisector in geometry?
3. Can you explain how to solve problems involving multiple bisectors in polygons?
4. How do you use the Angle Sum Property of a triangle in geometry problems?
5. What other methods could you use to verify the correctness of an angle bisector problem?

Tip: Whenever you are given a bisector, it splits the angle into two equal parts—always useful for calculating unknown angles in geometry.