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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Chapter Test

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Exercise 4 Page 211

Note that the lines cut by the transversal are parallel.

m∠ 1=65^(∘) (Corresponding Angles Theorem)
m∠ 2=65^(∘) (Alternate Interior Angles Theorem)

Practice makes perfect

To find m∠ 1, we can use the fact that 65^(∘) and ∠ 1 are corresponding angles. Therefore, by the Corresponding Angles Theorem, they are congruent. This means that m∠ 1= 65^(∘).

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

The ∠ 1 and ∠ 2 are vertical angles.
Angles 65^(∘) and ∠ 1 are alternate interior angles.

Let's think about the second approach. By the Alternate Interior Angles Theorem, angles are congruent when the lines that are cut by the transversal are parallel. Therefore, angles 65 ^(∘) and ∠ 2 will have the same measure.