https://r2.erweima.ai/mathbot/image/1727182072985nfhjm5w4.jpg

what is the statement and reasoning of this question?

The statement in the image reads:

**"If ∠A is complementary to ∠B and ∠A is complementary to ∠C, then ∠B ≅ ∠C."**

Let's break this down:

### Reasoning:
1. **Complementary Angles**: Two angles are complementary if their sum is 90°. So, the fact that ∠A is complementary to both ∠B and ∠C means:
   - \( \angle A + \angle B = 90^\circ \)
   - \( \angle A + \angle C = 90^\circ \)

2. Since both pairs add up to 90°, we can equate the two sums:
   \[
   \angle A + \angle B = \angle A + \angle C
   \]

3. Subtracting \( \angle A \) from both sides:
   \[
   \angle B = \angle C
   \]

   This means ∠B and ∠C must be congruent (∠B ≅ ∠C).

### Conclusion:
- The statement is **true**.
- The reasoning comes from the **definition of complementary angles** and simple algebraic manipulation.

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Do you have any questions or need more details?

### Related Questions:
1. What are complementary angles and how are they different from supplementary angles?
2. Can you explain how the concept of congruent angles is used in geometry?
3. What is the difference between complementary and congruent angles?
4. How would this reasoning change if the angles were supplementary instead of complementary?
5. Can you provide another example of complementary angles in a different geometric context?

### Tip:
Whenever you deal with complementary or supplementary angles, always think of the total degrees they sum up to: 90° for complementary and 180° for supplementary!

What is the statement and reasoning of this question?

This geometry problem explains how two angles that are complementary to the same angle must be congruent. Learn how complementary angles work, the formula for angle sums, and the congruence of angles. Suitable for students in Grades 6-8.

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