. Is the following statement a good definition? Why? An obtuse angle is an angle whose measure is greater than 90°. No, it is not. The statement contains false information. No, it is not. A straight angle has a measure greater than 90°, but it is not an obtuse angle. Yes, it is. The definition is reversible. Yes, it is. All obtuse angles have measures greater than 90°.
Yes, it is. All obtuse angles have measures greater than 90°, and the reverse is also true: any angle with a measure greater than 90° is an obtuse angle.
No, the statement "An obtuse angle is an angle whose measure is greater than 90°" is not a good definition.
An obtuse angle is defined as an angle whose measure is greater than 90° but less than 180°. However, the statement in the question incorrectly suggests that all angles greater than 90° are obtuse. This is not true because angles with measures greater than 180° are not considered obtuse angles.
The correct answer is: Yes, it is. All obtuse angles have measures greater than 90°.
To understand why this statement is a good definition, let's break it down:
1. The definition accurately describes what an obtuse angle is by stating that its measure is greater than 90°. This aligns with the common definition of an obtuse angle.
2. The statement is accurate and not false. An obtuse angle is indeed an angle greater than 90°.
3. The definition is reversible, which means that it can also be used to identify obtuse angles in real-world scenarios. For example, when given an angle with a measure greater than 90°, you can confidently say that it is an obtuse angle.
Overall, this definition is clear, accurate, and provides a solid understanding of what constitutes an obtuse angle.