Question

lines a, b, c, and d are shown below and c || d. what is the value of x?
a 60
b 90
c 110
d 130

Explanation:

Step1: Find the exterior angle of \(120^{\circ}\)

The exterior angle of \(120^{\circ}\) is \(180 - 120=60^{\circ}\) (supplementary angles).

Step2: Use the property of triangle exterior angle

The sum of two non - adjacent interior angles of a triangle is equal to the exterior angle. Let's assume the triangle formed by the intersection of lines \(a\), \(b\), \(c\) and \(d\). The two non - adjacent interior angles of the triangle (with respect to the exterior angle \(x\)) are \(50^{\circ}\) and \(60^{\circ}\). Then \(x = 50+60 = 110^{\circ}\) (triangle exterior angle theorem).

Answer:

C. \(110\)