2. Parallel Lines and Transversals
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What applies to corresponding, alternate exterior, alternate interior, and consecutive interior angles when the lines that are cut by the transversal are parallel?
∠ 2=100^(∘)
∠ 3=80^(∘)
∠ 4=100^(∘)
∠ 5=80^(∘)
∠ 6=100^(∘)
∠ 7=80^(∘)
∠ 8=100^(∘)
Let's draw the figure for ourselves and then we can start classifying each of the angles.
If two parallel lines are cut by a transversal, any corresponding angles are congruent. Examining the figure, we notice that ∠ 1 and ∠ 5 are corresponding angles. If m∠ 1=80^(∘), it follows that m∠ 5=80^(∘).
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^(∘).
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^(∘).
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.
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.
