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Note that the lines cut by the transversal are parallel.
m∠1=123^(∘) (Linear Pair Postulate) m∠2=57^(∘) (Alternate Interior 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 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^(∘).
