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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Quiz

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Exercise 11 Page 146

Note that the lines cut by the transversal are parallel.

m∠ 1=123^(∘) (Linear Pair Postulate)
m∠ 2=57^(∘) (Alternate Interior Angles Theorem)

Practice makes perfect

To find m∠ 1, we can use the fact that 57^(∘) and ∠ 1 form a linear pair. By the Linear Pair Postulate, they are supplementary which means their measures add up to 180^(∘):

m∠ 1+57^(∘)= 180^(∘) ⇔ m∠ 1= 123^(∘). To find m∠ 2, we can either use the fact that 57^(∘) and ∠ 2 are alternate interior angles or we can use that ∠ 1 and ∠ 2 are consecutive interior angles. If we go with the Alternate Interior Angles Theorem, we know that these angles are congruent. m∠ 2= 57^(∘).

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Exercises p.146