Question

Use the conditional: If $m\angle 1=120$, then∠1 is obtuse.

Provide a counterexample to disprove the converse.

Short answer

The counterexample to disprove the converse is if $m\angle 1=130$, then still ∠1 is obtuse.

Step-by-step solution

Step 1. Description of step.

In the conditional statement, the hypothesis is the statement written after the word if.

In the conditional statement, the conclusion is the statement written after the word then.

The converse of the conditional can be found out by interchanging the hypothesis and the conclusion.

The example for which a hypothesis is true and the conclusion is false is called a counterexample.

Step 2. Description of step.

It is being given that if$m\angle 1=120$, then∠1 is obtuse.

Therefore it can be seen that the statement written after the word if is$m\angle 1=120$ and the statement written after the word then is∠1 is obtuse.

Therefore, the hypothesis of the conditional statement is$m\angle 1=120$ and the conclusion of the conditional statement is∠1 is obtuse.

The conditional after interchanging the hypothesis and conclusion is if∠1 is obtuse then $m\angle 1=120$.

Therefore, the converse is if∠1 is obtuse then $m\angle 1=120$.

If $m\angle 1=130$, then still∠1 is obtuse.

Therefore, if $m\angle 1=130$, then hypothesis is true but conclusion is false.

Therefore, the counterexample to disprove the converse is if $m\angle 1=130$, then still ∠1 is obtuse.

Step 3. Write the counterexample to disprove the converse.

The counterexample to disprove the converse is if $m\angle 1=130$, then still ∠1 is obtuse.