Find the value of y for which line a is parallel to line b

38

52

76

142

As is shown in the figure attached:

1. "A" and 76º are congruents, because they are Alternate Interior angles, so A=76º.
 
 2. "D" and "x" are congruents, because they are Alternate Interior angles, so x=38º.
 
 3. "A", "B" and "C" form a the triangle ABC. Then, we remember sum of the interior angles of a triangle is 180º, so we have:
 
 76º+38º+B=180º
 B=180º-76º-38º
 B=66º
 
 4. By definition, an exterior angle of a triangle is equal to the sum of the opposite interior angles to it. So, we can calculate the exterior angle "y" of the triangle ABC, as follows:
 
 The opposite angles are: 76º and 66ª. Then, we obtain:
 
 y=76º+66º
 y=142º

 Therefore, the answer is: The value of y is 142º.