Final answer:
Option C (an angle that is 75 degrees) is NOT a counterexample of the conjecture 'If an angle is obtuse, then it is 100 degrees,' because an obtuse angle must be greater than 90 degrees and a 75-degree angle is acute, not obtuse.
Step-by-step explanation:
The conjecture states: If an angle is obtuse, then it is 100 degrees. A counterexample to this conjecture is an angle that is obtuse, but not equal to 100 degrees, which disproves the conjecture. The options given are:
- A) an angle that is 120 degrees
- B) An angle that is 165 degrees
- C) An angle that is 75 degrees
- D) An angle that is 95 degrees
Options A and B are counterexamples since 120 and 165 degrees are both obtuse angles but not equal to 100 degrees. Option C is not a counterexample because 75 degrees is not an obtuse angle (obtuse angles are greater than 90 degrees but less than 180 degrees). Option D could be considered a counterexample since a 95-degree angle is obtuse, but it is very close to the conjecture being tested and may not clearly illustrate its falsehood. Therefore, the correct answer is C) An angle that is 75 degrees, as it does not provide a counterexample to the given conjecture.