Question

Consider the following conditional statement. Determine the contrapositive

of the statement and then determine if the contrapositive is true or false.
If two angles are not complements, then their measures do not add up to 180°.

The contrapositive of the statement is true.
The contrapositve of the statement is false.

Answer 1

The contrapositive of the statement is true.

Explanation:

For a general statement:

p ⇒ q

The contrapositive statement is:

¬q ⇒ ¬p

where:

¬q is the negation of the proposition q.

Here we have the statement:

If two angles are not complements, then their measures do not add up to 180°

So we have:

p = two angles are not complements

q = their measures do not add up to 180°

Then the negations are:

¬p = two angles are complements

¬q = their measures do add up to 180°

The contrapositive statement is:

"if for two angles their measures do add up to 180°, then the two angles are complements"

This is true, if for two angles the sum of their measures is equal to 180°, then these angles are complementary.

Then: The contrapositive of the statement is true.