Question

Complete the two-column proof for the given statement: If two angles are supplementary, then the sum of their measures is 180 degrees. Provide the step-by-step solution.

Answers

GPT-4o mini
To complete the two-column proof for the statement "If two angles are supplementary, then the sum of their measures is 180 degrees," we will structure the proof into statements and reasons.

**Two-Column Proof:**

| **Statements** | **Reasons** |
|------------------------------------------------------------|----------------------------------------------------------|
| 1. Let angle A and angle B be two supplementary angles. | 1. Given (definition of supplementary angles). |
| 2. By definition of supplementary angles, A + B = 180°. | 2. Definition of supplementary angles (two angles that add up to 180°). |
| 3. Therefore, the sum of the measures of angle A and angle B is 180 degrees. | 3. Conclusion based on the definition provided in step 2. |

**Explanation:**

1. We start with two angles \( A \) and \( B \), which we define to be supplementary.
2. According to the definition of supplementary angles, the sum of the measures of these angles must equal \( 180° \) (this is the definition itself).
3. We conclude that since the angles are defined to be supplementary, their sum must indeed be 180 degrees, which directly follows from the definition.

This completes the proof, illustrating the relationship between supplementary angles and their sum.