Question

which diagram shows a pair of angle measures that proves lines g and h are parallel? a b c d

Explanation:

Step1: Recall the property of supplementary angles

If two lines are cut by a transversal and the consecutive interior angles are supplementary (\(a + b=180^{\circ}\)), then the two lines are parallel.

Step2: Analyze option A

In option A, \(125^{\circ}+55^{\circ}=180^{\circ}\). These two angles are consecutive interior angles. According to the consecutive - interior - angles - converse theorem, if \(m\angle1 + m\angle2 = 180^{\circ}\) (where \(\angle1\) and \(\angle2\) are consecutive interior angles formed by a transversal intersecting two lines), then the two lines are parallel.

Step3: Analyze option B

The angles in option B are not in a position (such as consecutive interior, corresponding, or alternate interior) that can be used to prove the lines \(g\) and \(h\) are parallel.

Step4: Analyze option C

The angles in option C are not in a position (such as consecutive interior, corresponding, or alternate interior) that can be used to prove the lines \(g\) and \(h\) are parallel.

Step5: Analyze option D

The angles in option D are not in a position (such as consecutive interior, corresponding, or alternate interior) that can be used to prove the lines \(g\) and \(h\) are parallel.

Answer:

A.