Question

question 8 of 10 in the diagram below, \\( \overline { a b } \\) is parallel to \\( \overline { c d } \\). what is the value of \\( y \\)? a. 30 b. 60 c. 50 d. 150

Explanation:

Step1: Find the adjacent angle of \(150^{\circ}\)

Since the sum of adjacent angles on a straight line is \(180^{\circ}\), the adjacent angle of \(150^{\circ}\) is \(180 - 150=30^{\circ}\)

Step2: Use the property of parallel lines

Because \(\overline{AB}\parallel\overline{CD}\), \(y\) and the adjacent angle of \(150^{\circ}\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(y = 30\)

Answer:

A. 30