MATH SOLVE

3 months ago

Q:
# Use the conditional statement to answer the question.If an angle is a right angle, then the angle measures 90°.Are the statement and its contrapositive true?Both the statement and its contrapositive are false.The statement is true, but the contrapositive is false.The statement is false, but the contrapositive is true.Both the statement and its contrapositive are true.

Accepted Solution

A:

The original statement is true by the definition of what constitutes a right angle. It's simply set up this way.

The contrapositive would be the statement "if the angle does not measure 90 degrees, then the angle is not a right angle" which is also a true statement. Example: a 37 degree angle is not a right angle.

Note: the original conditional "If P, then Q" would have the contrapositive be in the form "If not Q, then not P". We flip P and Q, and stick "not"s in front of both parts.

So this is why the answer is choice D

The contrapositive would be the statement "if the angle does not measure 90 degrees, then the angle is not a right angle" which is also a true statement. Example: a 37 degree angle is not a right angle.

Note: the original conditional "If P, then Q" would have the contrapositive be in the form "If not Q, then not P". We flip P and Q, and stick "not"s in front of both parts.

So this is why the answer is choice D