Let's start by looking at ∠1 and ∠3 and how they can be paired with the known angle. In the first figure, ∠1 and 80^(∘) are consecutive interior angles. In the second figure, ∠3 and 80^(∘) are consecutive interior angles.
According to the Consecutive Interior Angles Theorem, such angles are supplementary if the lines that are cut by the transversal are parallel. Since the lines are parallel, we have that
m∠1+80^(∘)=180^(∘) &⇔ m∠1=100^(∘)
m∠3+80^(∘)=180^(∘) &⇔ m∠3=100^(∘).
To find the remaining angle, we let a new line make the transversal.
Again ∠1 and ∠2 are consecutive interior angles and, like already explained, they are supplementary if the lines cut by the transversal are parallel. Therefore we have:
m∠2=80^(∘).
