Question

The conditional statement"If mC- 97°, then 2C is obtuse" is true. Which of the following statements must also be true? 1. If ZC is obtuse, then m_C= 97º. 2. IfZC is not obtuse, then mzC979.3. IF mZC+970, then ZC is not obtuse.

A. 1 and 2 only
B. 2 and 3 only
C. 2 only
D. 3 only ​

Answer 1

To determine which statements are true, we need to analyze the given conditional statement carefully. The original statement is: "If m<C = 97°, then 2<C is obtuse." The only true statement is: If m<ZC + 97°, then Z<C is not obtuse.

Step-by-step explanation:

To determine which statements are true, we need to analyze the given conditional statement carefully. The original statement is: "If m<C = 97°, then 2<C is obtuse."

1. If Z<C is obtuse, then m<C = 97°: This statement is the converse of the original statement. The converse is not always true, so we cannot conclude that this statement is necessarily true.
2. If Z<C is not obtuse, then m<C > 97°: This statement is the inverse of the original statement. The inverse is not always true, so we cannot conclude that this statement is necessarily true.
3. If m<ZC + 97°, then Z<C is not obtuse: This statement is the contrapositive of the original statement. The contrapositive is always true if the original statement is true, so we can conclude that this statement is true.

Therefore, the correct answer is D. 3 only.