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To solve this question, we need to determine which angle is complementary to \( \angle EBD \). Two angles are complementary if their measures add up to \(90^\circ\).

### Step-by-Step Approach:
1. \( \angle EBD \) is the angle formed between line segments \( \overrightarrow{BE} \) and \( \overrightarrow{BD} \), which appears to be less than \(90^\circ\).
2. The angle complementary to \( \angle EBD \) must add up to \( 90^\circ \) with it. From the diagram, we can see that \( \angle ABC \) (the angle between \( \overrightarrow{BA} \) and \( \overrightarrow{BC} \)) is a right angle, which implies that:
   \[
   \angle ABC = 90^\circ.
   \]
   
Since \( \angle ABC \) forms a right angle at point \( B \) with one of its sides overlapping \( \overrightarrow{BD} \), the angle complementary to \( \angle EBD \) must be \( \angle ABC \).

### Conclusion:
The angle complementary to \( \angle EBD \) is \( \angle ABC \).

Do you want further details, or have any other questions?

### Related Questions:
1. How do complementary angles differ from supplementary angles?
2. Can an obtuse angle ever be complementary to another angle?
3. How do you determine whether angles are complementary when the measures aren't obvious?
4. How does the diagram show that \( \angle ABC \) is a right angle?
5. Why is the sum of complementary angles always \( 90^\circ \)?

### Tip:
Complementary angles are typically found in geometric figures involving right angles or perpendicular lines. Always look for these clues in diagrams.

Explore how to determine which angle is complementary to ∠EBD using the concept of complementary angles. This problem involves identifying complementary angles and understanding how the sum of these angles forms 90°. Suitable for students in Grades 6-8.

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