Question

Explain whether the following statement is a valid definition: “A 150° angle is an obtuse angle.” Use the converse, biconditional, and at least one Euler diagram to support your answer.

Answer 1

If this "“A 150° angle is an obtuse angle" is a definition for obtuse angle, then the statement AND its converse must both be true.

Original statement in IF, Then form:


p: If an angle has measure 150
q: then the angle is obtuse.

That is true.

Converse:

q --> p

If an angle is obtuse, then the angle has measure 150.

That is NOT true because an obtuse angle has measure greater that 90. The obtuse angle could be 130 for all we know.


Because the converse is false, the statement : “A 150° angle is an obtuse angle" is NOT a valid definition of an obtuse angle.

Answer 2

The angle 150 is one of infinitely many angle measures that could be labeled as an obtuse angle.



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