https://file.aiquickdraw.com/mathbot/file/1728922753977r74d4g81.jpg

The problem asks to find a counterexample to the statement: "If two angles are supplementary, then one of the angles must be obtuse."

**Supplementary angles** are two angles whose sum is 180°. A counterexample would show two supplementary angles where neither angle is obtuse (an obtuse angle is greater than 90° but less than 180°).

Upon reviewing the provided images:

- **A**: Shows two angles, both acute (less than 90°), but not forming supplementary angles.
- **B**: Shows two angles that are both **right angles (90°)**. These angles are supplementary because \(90^\circ + 90^\circ = 180^\circ\), and neither is obtuse.
- **C**: Shows one acute angle and one obtuse angle, but this supports the original statement, not a counterexample.
- **D**: Involves an obtuse angle and another acute angle, also supporting the original statement.

### The correct answer is **B**, because it shows two right angles that sum to 180° without either being obtuse, providing a counterexample to the given statement.

Would you like further clarification or additional details? Here are 5 questions to deepen understanding:

1. What are supplementary angles, and how are they defined?
2. How do acute, obtuse, and right angles differ?
3. Can two acute angles ever be supplementary? Why or why not?
4. Why does an obtuse angle plus an acute angle often result in supplementary angles?
5. How do we formally prove or disprove statements using counterexamples in geometry?

**Tip:** When proving or disproving geometric statements, always test edge cases like right angles or multiples of 90°.

If two angles are supplementary, then one of the angles must be obtuse. Which image provides a counterexample to this statement?

Find the counterexample that disproves the statement 'If two angles are supplementary, then one of the angles must be obtuse.' Understand how right angles can be supplementary without being obtuse. Suitable for Grades 6-8.

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