Question

Is the following statement a good definition? Why?

An obtuse angle is an angle whose measure is greater than 90°.
A No, it is not. The statement contains false information.
B Yes, it is. The definition is reversible.
C Yes, it is. All obtuse angles have measures greater than 90°.
D No, it is not. A straight angle has a measure greater than 90°, but it is not an obtuse angle.

Answer 1

D No, it is not. A straight angle has a measure greater than 90°, but it is not an obtuse angle.
The sentence should say: An obtuse angle is an angle whose measure is greater than 90° but less than 180°

Answer 2

The correct option is D.

Explanation:

An an angle is called an obtuse angle if the measure of angle is lies between 90° and 180°. The angle θ is an obtuse angle if

`90^(\circ)<\theta<180^(\circ)`

The given statement is "An obtuse angle is an angle whose measure is greater than 90°."

It is an false statement, because all angles whose measure is more than 90°, are not an obtuse angle.

For example the angle 200° is more than 90° but not less than 180°, therefore the angle 200° is not an obtuse angle. The angle 180° is not an obtuse angle.

Therefore option D is correct.