Exercise 10 Page 518

Note that the lines cut by the transversal are parallel.

m∠ 1=123^(∘) (Alternate Exterior Angles Theorem)
m∠ 2=123^(∘) (Vertical Angles Congruence Theorem)

Practice makes perfect

To find m∠ 2, we can use the fact that 123^(∘) and ∠ 2 are vertical angles. By the Vertical Angles Congruence Theorem, they are congruent. This means they have the same measure! m∠ 2=123^(∘). To find m∠ 1, we can either use the fact that 123^(∘) and ∠ 1 are corresponding angles, or that ∠ 1 and ∠ 2 are alternate interior angles. Since the lines cut by the transversal are parallel, we can, by the Corresponding Angles Theorem and the Alternate Exterior Angles Theorem, say that these pairs of angles will be congruent. Therefore, we have that m∠ 2=123^(∘).

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