Question

If an angle is obtuse, then the angle measures 98°. Which of the following are true?

I. The statement is true.
II. The converse of the statement is true.
III. The contrapositive of the statement is true.

a. I only
b. II only
c. III only
d. I and II
e. I and III

Answer 1

The statement that if an angle is obtuse and measures 98° is true, but the converse of the statement is false. Option a) is correct.

Step-by-step explanation:

The statement is true.

An obtuse angle is an angle greater than 90 degrees but less than 180 degrees. If an angle is obtuse and measures 98°, then it falls within the range of being greater than 90 degrees and less than 180 degrees, satisfying the definition of an obtuse angle. Therefore, the statement is true.

The converse of the statement is false.

The converse of the statement is: If an angle measures 98°, then it is obtuse. However, an angle measuring 98° can also be acute (less than 90 degrees), violating the definition of an obtuse angle. Therefore, the converse of the statement is false.