Question

What must be the value of x so that lines c and d are parallel lines cut by transversal p?

Answer 1

Check the picture below.

since "y" and 3x+45 are both linear angles, then y + (3x + 45) = 180.

but wait a second!!  "y" is a corresponding angle to 81°, so y = 81° then, therefore,

$\bf y+(3x+45)=180\implies 81+(3x+45)=180 \\\\\\ 126+3x=180 \implies 3x=54\implies x=\cfrac{54}{3}\implies x=18$

and that can only happen, if c || d.

Answer 2

18      is the correct answer