Question

problem 22: (first taught in lesson 26) select the converse of this statement, and determine whether it is true or false. if two angles are a linear pair, then they are supplementary.

Explanation:

Step1: Define converse

The converse of a conditional statement "If p, then q" is "If q, then p". Here, p = "two angles are a linear pair" and q = "they are supplementary". So the converse is "If two angles are supplementary, then they are a linear - pair".

Step2: Analyze truth - value

Supplementary angles are two angles whose sum is 180 degrees. A linear pair of angles are adjacent angles that form a straight line (sum to 180 degrees). But two non - adjacent angles can also be supplementary. For example, two angles in different parts of a room that measure 120 degrees and 60 degrees are supplementary but not a linear pair. So the converse is false.

Answer:

Converse: If two angles are supplementary, then they are a linear - pair. False.