Two adjacent angles represent a linear pair when their non-common sides are opposite rays — a straight line, whose measure is 180^(∘). This means that a linear pair is a pair of supplementary angles. Now we can create if-then statements that allow us to find the angle measures.
if-then statements
Note that ∠ 2 is a linear pair with ∠ 1.
If& ∠ 2 is a linear pair with ∠ 1,
then& ∠ 2 is supplementary to ∠ 1.
If& ∠ 2 is supplementary to ∠ 1 and m∠1 = 90^(∘),
then& m∠ 2 = 90^(∘).
Using the same logic, we can say that ∠ 4 is a linear pair to ∠ 1.
If& ∠ 4 is a linear pair with ∠ 1,
then& ∠ 4 is supplementary to ∠ 1.
If& ∠ 4 is supplementary to ∠ 1 and m∠1 = 90^(∘),
then& m∠ 4 = 90^(∘).
Continuing, we can say that ∠ 3 is a linear pair to either ∠ 2 or ∠ 4.
If& ∠ 3 is a linear pair with ∠ 2,
then& ∠ 3 is supplementary to ∠ 2.
If& ∠ 3 is supplementary to ∠ 2 and m∠2 = 90^(∘),
then& m∠ 3 = 90^(∘).
