Question

let statements p, q, r, and s be as follows: p: ∠a and ∠b are a linear pair. q: ∠a and ∠b are supplementary angles. r: ∠a and ∠b are adjacent angles. s: ∠a and ∠b are adjacent and supplementary angles. substitute for p, q, r, or s, and write the statement the way you would read it. p→s choose the correct answer below. a. if ∠a and ∠b are adjacent and supplementary angles, then ∠a and ∠b are a linear pair. b. if ∠a and ∠b are adjacent and supplementary angles, then ∠a and ∠b are adjacent and supplementary angles. c. if ∠a and ∠b are a linear pair, then ∠a and ∠b are adjacent and supplementary angles. d. if ∠a and ∠b are a linear pair, then ∠a and ∠b are adjacent and supplementary angles.

Explanation:

Step1: Recall definitions

Linear - pair angles are adjacent and supplementary. Supplementary angles add up to 180 degrees and adjacent angles share a common side and a common vertex.

Step2: Analyze the statements

The statement \(p
ightarrow s\) means if \(p\) ( \(\angle A\) and \(\angle B\) are a linear - pair) is true, then \(s\) ( \(\angle A\) and \(\angle B\) are adjacent and supplementary) is true. By the definition of a linear - pair, if two angles are a linear - pair, they are adjacent and their sum is 180 degrees (supplementary).

Answer:

A. If \(\angle A\) and \(\angle B\) are adjacent and supplementary, then \(\angle A\) and \(\angle B\) are a linear pair.