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. s→p 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 a linear pair, then ∠a and ∠b are adjacent and supplementary angles. c. ∠a and ∠b are adjacent and supplementary angles if and only if ∠a and ∠b are a linear pair. d. ∠a and ∠b are a linear pair if and only if ∠a and ∠b are adjacent and supplementary angles.

Explanation:

Step1: Recall definitions

Linear - pair angles are adjacent and supplementary. The statement $s
ightarrow p$ means if $s$ then $p$. Here, $s$ is “$\angle A$ and $\angle B$ are adjacent and supplementary angles” and $p$ is “$\angle A$ and $\angle B$ are a linear - pair”.

Step2: Analyze conditional statement

By the definition of linear - pair angles, if two angles are adjacent and supplementary, then they are a linear pair.

Answer:

A. If $\angle A$ and $\angle B$ are adjacent and supplementary angles, then $\angle A$ and $\angle B$ are a linear pair.