If two parallel lines are cut by a transversal, any alternate interior angles are congruent. Examining the figure, we notice that ∠5 and ∠3 are alternate interior angles. Therefore, if m∠5=80^(∘), we must have m∠3=80^(∘).
Alternate Exterior Angles
If two parallel lines are cut by a transversal, any alternate exterior angles are congruent. Examining the figure, we notice that ∠1 and ∠7 are alternate exterior angles. Therefore, if m∠1=80^(∘), it is also true that m∠7=80^(∘).
Consecutive Interior Angles
If two parallel lines are cut by a transversal, any consecutive interior angles are congruent. Examining the figure, we notice that ∠2 and ∠5 are consecutive interior angles and so are ∠3 and ∠8. Therefore, if m∠3= 80^(∘) and m∠5= 80^(∘) we can solve for these unknown angles.
m∠2+ 80^(∘) &= 180^(∘) ⇔ m∠2=100^(∘)
m∠8+ 80^(∘)&= 180^(∘) ⇔ m∠8=100^(∘)
Let's mark these angles in our figure.
Remaining Angles
The remaining angles can be determined in a number of different ways. For example, we can use the fact that ∠4 and ∠1 are a linear pair and so are ∠5 and ∠6. This means that they are supplementary angles and their measures add up to 180.
m∠4+ 80^(∘) &= 180^(∘) ⇔ m∠4=100^(∘)
m∠6+ 80^(∘)&= 180^(∘) ⇔ m∠6=100^(∘)
Let's finish our figure.
