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Answered

If an angle is obtuse, then its measure is 150°.
CONVERSE
INVERSE
CONTAPOSITIVE​

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Answer:

CONVERSE

  • If it measures 150° then it is an obtuse angle.

INVERSE

  • Obtuse angle also vary

CONTRAPOSITIVE

  • 150° is an obtuse angle.

Step-by-step explanation:

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IF-THEN STATEMENTS

Given:

If an angle is obtuse, then its measure is 150°.

Answers:

CONVERSE - If an angle measures 150°, it is obtuse.

INVERSE - If an angle is not obtuse, then it does not measure 150°.

CONTRAPOSITIVE - If an angle does not measure 150°, it is not obtuse.

Step-by-step explanation:

The given statement is an example of a conditional (statement).

Conditional statement is a statement that consists a hypothesis and a conclusion. This could be express as 'p → q' or 'p ⇒ q' where p is the first premises in Law of Detachment (hypothesis) and q for the conclusion. p ⇒ q is read as 'p implies q'. Implies use for that symbol (right arrow). When it is expressed in a sentence, that would be like this: If p, then q. Hypothesis is after the word 'if' while conclusion after the word 'then'.

Converse statement is a statement that interchange the hypothesis and the conclusion of a conditional statement. Hence, 'q → p' or 'q ⇒ p'. The conclusion implies the hypothesis.

For example: The given conditional into converse

The statement would interchange to be called converse. Thus, it is "If an angle measures 150°, it is obtuse."

Inverse statement is a statement that negating both hypothesis and conclusion in a conditional. Hence, "If not p, then not q." or '~p → ~q'. The symbol ~ is used when using the word 'not'.

Given the example conditional into inverse:

Both part of p and q which are after 'if' and 'then' would be negate. Thus, it is "If an angle is not obtuse, then it does not measure 150°."

Lastly. contrapositive statement is a statement that interchange the hypothesis and the conclusion of an INVERSE. Hence. "If not q, then not p." or '~q → ~p'.

Referring to the given conditional as contrapositive

It would be interchange and then, would negate. Thus, it is "If an angle does not measure 150°, it is not obtuse."

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