Question

state the truth statement of the conditional. then choose the correct form of the inverse of the conditional statement and state the truth - value for the inverse. conditional statement: \if the sum of two angles is 180°, then the angles are a linear pair.\ true or false? inverse: inverse true or false?

Explanation:

1. Recall the definition of a linear - pair of angles: A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays and the sum of the angles in a linear pair is 180°. But just because the sum of two angles is 180°, they may not be adjacent. So the conditional statement "If the sum of two angles is 180°, then the angles are a linear pair" is False.
2. The inverse of a conditional statement "If p, then q" is "If not p, then not q". Here, p is "the sum of two angles is 180°" and q is "the angles are a linear pair". So the inverse is "If the sum of two angles is not 180°, then the angles are not a linear pair". Since a linear pair has a sum of 180°, if the sum is not 180°, they cannot be a linear pair. So the inverse is True.

Answer:

Conditional Statement True or False: False
Inverse: If the sum of two angles is not 180°, then the angles are not a linear pair
Inverse True or False: True