Question

Find the measure of <2. Justify your answer.

A. m<2 =75 because same-side interior angles of parallel lines are congruent.
B. m<2=105 because same-side interior angles of parallel lines are supplementary.
C. m<2=75 because same-side interior angles of parallel lines are supplementary.
D. m<2 =105 because same-side interior angles of parallel lines are congruent.

Answer 1

m<2=105

Explanation:

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Answer 2

The answer is: B. m∠2=105 because same-side interior angles of parallel lines are supplementary.

The explanation is shown below:

1. By definition, when two parallel lines are cut by a transversal, which is another line. And the same-side interior angles of parallel lines are supplementary.

3. The angle that measures 75 degrees and the angle m∠2 are supplementary, which means that the sum of both are 180 degrees.

4. Therefore, you have the following result:

`180-75=105`

3. Then m∠2 measures 105 degrees.