Find a counterexample that demonstrates that the converse of If two angles measure 32° and 148°, then they are supplementary Is false

The original statement is: "If two angles measure 32° and 148°, then they are supplementary."

To find the converse, we reverse the statement:

**Converse Statement:** "If two angles are supplementary, then they measure 32° and 148°."

A counterexample would be any pair of supplementary angles that do not measure 32° and 148°.

### Counterexample:
Let's take the angles 60° and 120°. These two angles are supplementary because their sum is \( 60° + 120° = 180° \). However, they do not measure 32° and 148°.

Thus, the converse statement is false because there are many pairs of supplementary angles other than 32° and 148°.

Would you like more details or have any questions?

Here are 5 related questions to think about:

1. What is the definition of supplementary angles?
2. Can two angles be supplementary if one of them is greater than 180°?
3. How do you determine if a given pair of angles is supplementary?
4. What is the converse of the statement “If two angles are complementary, then they add up to 90°”?
5. Can you give an example of two angles that are not supplementary but still form a linear pair?

**Tip:** When determining if the converse of a statement is true, always try to find a counterexample to see if there are exceptions.

Find a counterexample that demonstrates that the converse of 'If two angles measure 32° and 148°, then they are supplementary' is false.

Discover how to find a counterexample for the converse of the statement 'If two angles measure 32° and 148°, then they are supplementary.' Learn about supplementary angles, converse statements, and explore a detailed solution with a real counterexample, suitable for Grades 6-8.

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