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Tell whether each statement is true or false. Then write converse and tell whether it is true or false.

Statement: If mT=40then Tis not obtuse.

Short Answer

Expert verified

The statement 鈥淚f mT=40,thenT is not obtuse.鈥 is true, but the converse 鈥淚fT is not obtuse then mT=40.鈥 is false.

Step by step solution

01

Step 1. Converse of a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement 鈥淚f p, then q鈥 will be 鈥淚f q, then p鈥.

02

Step 2. State whether the statement is true or not.

Here, mT=40, thus, theT is less than 90.

So, Tis not obtuse, as, an angle that is more than 90and less than 180, is called an obtuse angle. Hence, the statement is true.

03

Step 3. Write converse of the statement and verify.

The converse of the statementT is: If is not obtuse then mT=40.

Here, if Tis not obtuse, then, mTis between 0and 90. So, it is not necessary that is equal to Thus, the converse statement is false.

Therefore, the statement: "If mT=40thenT is not obtuse" is true, but the converse of the statement: "T If is not obtuse then mT=40," is false.

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