Let's fill in the missing reasons:

Statements	Reason

1. ∠1≅∠5 | 1. Given
2. ∠2≅∠5 | 2. Vertical Angles Theorem
3. ∠1≅∠2 | 3. Transitive Property of Equality (since ∠1≅∠5 and ∠2≅∠5, we have ∠1≅∠2)
4. ∠1≅∠4 | 4. Vertical Angles Theorem (since ∠1 and ∠4 are vertical angles)
5. ∠2≅∠4 | 5. Transitive Property of Equality (since ∠1≅∠2 and ∠1≅∠4, we have ∠2≅∠4)

This completes the proof.

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

Related Questions:

1. What is the Transitive Property of Equality in geometry?
2. How are vertical angles defined?
3. Can you explain how to identify congruent angles using properties of vertical angles?
4. How does one identify corresponding angles in a geometric diagram?
5. What other properties can be used to prove congruence of angles?

Tip: When proving statements in geometry, always establish clear relationships between the angles or segments using given properties or theorems.