Assume that lines that appear to be parallel are parallel. find the value of x and the measure of angle y

What information have we been given here? From the diagram, we can see that (9x+1)° and (14x-34)° degrees are supplementary, meaning:

(9x+1)+(14x-34)=180

There, we have an equation we can fairly easily solve for x. What about y?

If we take a look at the line y° occupies, we can see that it shares a straight angle with our (14x-34)° term and - as implied by the right angle on the bottom line - a 90° angle.

All three of these should add up to 180°, so we have:

(14x-34) + y + 90 = 180

Another think to note is that, upon inspection, (14x-34)° and y° are complementary - they add up to 90° - and subtracting the 90 from both sides of our equation confirms that fact:

(14x-34) + y = 90

If you've solved for x prior to this, solving for y should be pretty straightforward.

Logical equivalent of the give question is its contrapositive