Question

lines a, b, c, and d are shown below, such that c || d. what is the value of y?
a 50
b 70
c 110
d 180

Explanation:

Step1: Find the angle adjacent to \(110^{\circ}\)

The sum of adjacent angles on a straight line is \(180^{\circ}\). Let the adjacent angle be \(x\). So, \(x + 110^{\circ}=180^{\circ}\), then \(x = 180^{\circ}- 110^{\circ}=70^{\circ}\).

Step2: Use the property of parallel lines

Since \(c\parallel d\), and we consider the trans - versal line. The angle \(x = 70^{\circ}\) and \(y\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So \(y=x\).

Answer:

A. \(50\) is incorrect. B. \(70\) is correct. C. \(110\) is incorrect. D. \(180\) is incorrect. So the answer is B. \(70\)