Question

practice using logical reasoning. how can the statement below be rewritten as a conditional statement in if - then form? two angles with angle measures that add up to 180 degrees form a linear pair. if two angles form a linear pair, then one of their angle measures is 180 degrees. if a linear pair has angle measures that add up to 180 degrees, then there are more than two angles. if the measures of two angles add up to 180 degrees, then they form a linear pair. if there are two angles, then their angle measures must add up to 180 degrees.

Explanation:

A conditional statement in if - then form has a hypothesis (the "if" part) and a conclusion (the "then" part). The original statement is about two angles whose measures add up to 180 degrees (hypothesis) and forming a linear pair (conclusion).

• Option 1: The hypothesis is wrong. A linear pair has two angles, not one with 180 degrees.
• Option 2: A linear pair has exactly two angles, so this is incorrect.
• Option 3: The hypothesis is "the measures of two angles add up to 180 degrees" and the conclusion is "they form a linear pair", which matches the original statement structure.
• Option 4: Not all pairs of angles add up to 180 degrees.

Answer:

C. If the measures of two angles add up to 180 degrees, then they form a linear pair.