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. ∠a and ∠b are a linear pair if and only if ∠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. if ∠a and ∠b are a linear pair, then ∠a and ∠b are adjacent and supplementary angles.

Explanation:

In logic, the symbol $\to$ represents a conditional statement "if - then". Here, $p$ is the antecedent and $s$ is the consequent. So $p\to s$ means if the statement $p$ is true, then the statement $s$ is true. Substituting the given statements for $p$ and $s$, we get "If $\angle A$ and $\angle B$ are a linear pair, then $\angle A$ and $\angle B$ are adjacent and supplementary angles".

Answer:

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