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Note that the lines cut by the transversal are parallel.
m∠ 1=42^(∘) (Linear Pair Postulate) m∠ 2=42^(∘) (Alternate Exterior Angles Theorem)
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 that ∠ 1 and ∠ 2 are consecutive interior angles. Since the lines cut by the transversal are parallel, we can, by the Alternate Exterior Angles Theorem, say that these angles are congruent. Therefore, we have that m∠ 2=123^(∘).
