Exercise 6 Page 507

Note that the lines cut by the transversal are parallel.

m∠ 1=140^(∘) (Alternate Interior Angles Theorem)
m∠ 2=40^(∘) (Consecutive Interior Angles Theorem)

Practice makes perfect

To find m∠ 1, we can use the fact that 140^(∘) and ∠ 1 are alternate interior angles. By the Alternate Interior Angles Theorem, they are congruent. Therefore, we have that m∠ 1= 140^(∘).

There are two approaches we can take to find the measure of m∠ 2.

The 140^(∘) angle and ∠ 2 are a linear pair.
Angles ∠ 1 and ∠ 2 are consecutive interior angles.

Let's think about the second approach. By the Consecutive Interior Angles Theorem, angles are supplementary when the lines that are cut by the transversal are parallel. Therefore, angles ∠ 1 and ∠ 2 will have measures that add to 180^(∘).

m∠ 1+m∠ 2=180

Substitute

m∠ 1= 140

140+m∠ 2=180

SubEqn

LHS-140=RHS-140

m∠ 2= 40^(∘)

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