Question

What is the value of x in the diagram?

Answer 1

The red arrows mean the lines are parallel. Since all angles are equal, the larger triangle is similar to the smaller one. Then corresponding sides have the same ratio
(4x -2)/9 = (3x+2)/12
x(4/9 -3/12) = (2/12) +(2/9)
x = (7/18)/(7/36) = 2 . . . . . . . . . corresponding to the 3rd selection