Question

which diagram below shows a pair of angle measures that prove lines a and b are parallel?
a
b
c
d

Explanation:

Step1: Recall parallel line theorems

If two lines are cut by a transversal and the corresponding angles are equal, then the lines are parallel.

Step2: Analyze each option

• Option A:

The angles \(130^{\circ}\) and \(130^{\circ}\) are corresponding angles. When corresponding angles are equal, by the corresponding angles postulate, lines \(a\) and \(b\) are parallel.

• Option B:

\(130^{\circ}\) and \(80^{\circ}\) are not equal and do not satisfy any of the parallel - line angle relationships (corresponding, alternate interior, alternate exterior, consecutive interior).

• Option C:

\(130^{\circ}\) and \(80^{\circ}\) are not equal and do not satisfy any of the parallel - line angle relationships (corresponding, alternate interior, alternate exterior, consecutive interior).

• Option D:

The \(130^{\circ}\) angles are on the same line \(a\) (they are vertical angles) and do not involve the relationship between lines \(a\) and \(b\) with respect to a transversal.

Answer:

A.