https://file.aiquickdraw.com/mathbot/file/1726894706923ynnlgu1e.jpg

Terrence's conjecture is that if two angles are supplementary, they must form a linear pair. A linear pair of angles is defined as two adjacent angles whose non-common sides form a straight line, summing up to 180°. 

Supplementary angles, however, are simply two angles that add up to 180°, but they do not necessarily need to be adjacent or form a straight line.

Let's examine each figure:

- **Figure A** shows a triangle with an interior angle. There's no clear indication of two angles being supplementary.
- **Figure B** consists of two separate right triangles. These angles do not seem to offer any supplementary pair.
- **Figure C** is a single right triangle. Again, there's no clear supplementary pair.
- **Figure D** shows two separate angles of 125° each. These angles are **not adjacent**, but they are **supplementary** since their sum equals 180°.

Thus, **Figure D** is a **counterexample** to Terrence’s conjecture. The two angles are supplementary but do not form a linear pair, proving that his conjecture is incorrect.

Would you like more details or have any further questions?

### Related Questions:
1. What is the difference between a linear pair and supplementary angles?
2. Can two right angles form a linear pair?
3. How can non-adjacent angles still be supplementary?
4. What are other examples of supplementary angles that are not a linear pair?
5. How does a counterexample disprove a mathematical conjecture?

### Tip:
In geometry, a counterexample is a powerful way to disprove a statement. One example that violates the conditions is enough to show the conjecture is false.

Terrence claims that if two angles are supplementary, then they are a linear pair. Which of the following figures is a counterexample to his conjecture?

This problem discusses a common misconception about supplementary angles. The conjecture claims that if two angles are supplementary, they must form a linear pair. A detailed solution identifies which figure serves as a counterexample, helping students understand the difference between supplementary angles and linear pairs.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation