Question

geometry - unit 1b summative - logic & venn diagrams (sy 2025 - 2026) drawing valid conclusions given the statements shown below, which of the following answer choices includes both the conclusion that can be drawn and the correct law for justifying it? 1) if two angles form a linear pair, then they are supplementary; 2) if two angles are supplementary, then the sum of their measures is 180°; 3) no valid conclusion can be drawn based on the information provided. o 3) therefore, if the sum of two angle measures is 180°, then they form a linear pair. justification: law of detachment o 3) therefore, if two angles are supplementary, then they form a linear pair. justification: law of syllogism o 3) therefore, if two angles form a linear pair, then the sum of their measures is 180°. justification: law of detachment o 3) therefore, if two angles form a linear pair, then the sum of their measures is 180°. justification: law of syllogism

Explanation:

Step1: Analyze linear pair statement

A linear pair's definition: adjacent angles with sum 180°, so they are supplementary. Justification: Law of Detachment.

Step2: Analyze supplementary angles statement

Supplementary angles' definition: sum of measures is 180°. Justification: Law of Detachment.

Answer:

1. Therefore, if two angles form a linear pair, then they are supplementary; Justification: Law of Detachment
2. Therefore, if two angles are supplementary, then the sum of their measures is 180°; Justification: Law of Detachment