Question

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Find the measure of ∠1. Justify your answer.


A.
m∠1 = 60 because same-side interior angles of parallel lines are supplementary.


B.
m∠1 = 60 because corresponding angles of parallel lines are supplementary.


C.
m∠1 = 120 because same-side interior angles of parallel lines are congruent.


D.
m∠1 = 120 because corresponding angles of parallel lines are congruent.

Answer 1

B. m∠1 = 60 because corresponding angles of parallel lines are supplementary.

This is the correct answer because when parallel lines are cut by a transversal, corresponding angles are congruent. In this case, ∠1 and ∠2 are corresponding angles, so m∠1 = m∠2. Also, the sum of the measures of two corresponding angles is 180 degrees, since they form a linear pair. Therefore, m∠1 + m∠2 = 180 degrees. Since m∠2 = 120 degrees (given), m∠1 = 60 degrees.