Question

find the measure of ∠2. justify your answer.

m∠2 = 105 because same - side interior angles of parallel lines are congruent.
m∠2 = 75 because same - side interior angles of parallel lines are supplementary.
m∠2 = 75 because same - side interior angles of parallel lines are congruent.
m∠2 = 105 because same - side interior angles of parallel lines are supplementary.

Explanation:

Step1: Recall angle - relationship rule

Same - side interior angles of parallel lines are supplementary, which means they add up to 180°.

Step2: Identify the given angle

The given angle adjacent to ∠2 is 75°.

Step3: Calculate the measure of ∠2

Let \(m\angle2=x\). Then \(x + 75^{\circ}=180^{\circ}\), so \(x=180^{\circ}-75^{\circ}=105^{\circ}\).

Answer:

D. \(m\angle2 = 105\) because same - side interior angles of parallel lines are supplementary.