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.