Question

problem 7: (first taught in lesson 26) determine whether this definition passes the reversibility test by writing its converse and determining whether the converse is true. then, select your answer. if two angles are a linear pair, then the sum of their measures is 180. a if the sum of the measures of two angles is 180, then the angles form a linear pair; converse is true and the definition passes. b c d e

Explanation:

Answer:

The answer is incorrect. The correct analysis is as follows:

Step1: Find the converse

The original statement is "If two angles are a linear pair, then the sum of their measures is 180". The converse is formed by switching the hypothesis and the conclusion, so the converse is "If the sum of the measures of two angles is 180, then the angles are a linear pair".

Step2: Determine if the converse is true

A linear pair of angles are adjacent and supplementary (sum to 180°). However, two angles can sum to 180° (be supplementary) without being adjacent (for example, two non - adjacent angles in a parallelogram that are supplementary). So the converse is false. Therefore, the definition does not pass the reversibility test. The option A is wrong because it claims the converse is true.
The correct answer should be that the converse is "If the sum of the measures of two angles is 180, then the angles form a linear pair" and the converse is false, so the definition does not pass the reversibility test. If we have to choose from the given option (assuming there are other options not fully shown but based on the error in option A), the answer related to the converse being false and the definition not passing would be correct. But based on the given option A, it is incorrect.