Question

is the following biconditional statement valid or not? \two angles form a linear pair if and only if they are supplementary.\ answer attempt 1 out of 3 valid not valid, conditional is false because you can have non - adjacent supplementary angles not valid, because two angles dont have to form a linear pair not valid, converse is false because you can have non - adjacent supplementary angles submit answer

Explanation:

Step1: Recall definitions

A linear - pair of angles are adjacent and supplementary. Supplementary angles are two angles whose sum is 180 degrees.

Step2: Analyze the biconditional

The biconditional statement "Two angles form a linear pair if and only if they are supplementary" has a conditional part "If two angles form a linear pair, then they are supplementary" (which is true) and a converse part "If two angles are supplementary, then they form a linear pair" (which is false). Non - adjacent angles can be supplementary, but they don't form a linear pair.

Answer:

Not Valid, Converse is false because you can have non - adjacent supplementary angles