Question

in the diagram below, which two lines are parallel?
type capital letters.
line type your answer... and type your answer...

Explanation:

Step1: Find the supplementary angles

For line \(A\), the supplementary angle of \(116^{\circ}\) is \(180 - 116=64^{\circ}\).
For line \(B\), the supplementary angle of \(123^{\circ}\) is \(180 - 123 = 57^{\circ}\).
For line \(C\), the supplementary angle of \(52^{\circ}\) is \(180 - 52=128^{\circ}\).
For line \(D\), the supplementary angle of \(64^{\circ}\) is \(180 - 64 = 116^{\circ}\).

Step2: Apply the parallel - line criterion (corresponding angles)

When two lines are cut by a transversal, if the corresponding angles are equal, the lines are parallel.
The supplementary angle of the angle formed by line \(A\) with the transversal is \(64^{\circ}\), and the angle formed by line \(D\) with the transversal is \(64^{\circ}\).

Answer:

Line \(A\) and Line \(D\)