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Sagot :
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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