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The question is asking for an evaluation of a statement regarding the definition of a straight angle, with a counterexample being provided in each option.

Let's break down the biconditional statement:
- A straight angle measures exactly **180 degrees**.
- An obtuse angle measures **between 90 and 180 degrees**.
- A reflex angle measures **between 180 and 360 degrees**.

### Reviewing the options:

- **Option A**: The biconditional is stated as "if an angle is a straight angle, then it has a greater measure than an obtuse angle." However, a counterexample given is a **reflex angle**, which is incorrect since a reflex angle is **greater than** 180 degrees. So, this option doesn't work.
  
- **Option B**: The biconditional is stated as "an angle is a straight angle if and only if it has a greater measure than an obtuse angle." A counterexample given is any **straight angle** with a measure less than an obtuse angle, which does not make sense, since **straight angles are 180 degrees**, which is more than any obtuse angle. So, this option is flawed.

- **Option C**: This option gives a similar statement as option A but mentions a **straight angle** with a measure less than an obtuse angle, which is incorrect. A straight angle cannot have a smaller measure than an obtuse angle. Hence, this is incorrect.

- **Option D**: The biconditional is stated as "an angle is a straight angle if and only if it has a greater measure than an obtuse angle." This is the correct formulation because a straight angle is exactly 180 degrees, and the counterexample is a **reflex angle**, which is indeed greater than 180 degrees.

### Conclusion:
The correct answer is **D**. The statement is a good definition, and a reflex angle (greater than 180 degrees) is a valid counterexample.

Would you like a more detailed explanation on any part? Here are some related questions you might want to explore:

1. What is the difference between a straight angle and an obtuse angle?
2. Can an angle be greater than a reflex angle?
3. What are the properties of a biconditional statement in geometry?
4. How are reflex angles used in geometry proofs?
5. Why are counterexamples important in mathematical definitions?

**Tip**: When evaluating a biconditional statement, ensure both "if" and "only if" parts are true for all possible cases.

The statement is not a good definition. The biconditional statement is 'if an angle is a straight angle, then it has a greater measure than an obtuse angle.' A counterexample to the statement is a reflex angle.

Explore how to evaluate biconditional statements in geometry with examples and counterexamples. Understand the properties of straight angles, obtuse angles, and reflex angles. This problem is suitable for students in Grades 7-10.

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