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.