Let's start with #3.
To find the variable y, we know that it is supplementary to an angle that is 38 degrees, meaning that it measures (180-38) degrees, which is equal to 142 degrees.
To find the variable x, we know that in relation to the angle labeled 38 degrees, angle x is a vertical angle, and all vertical angles are congruent, or have the same measure. Thus, the variable x equals 38 degrees.
So the answer to #3 is d. x = 38, y = 142.
Now, let's move on to #4
The diagram shows a right angle which measures 90 degrees (designated by the square symbol), an angle that measures x degrees, and an angle that measures 56 degrees. We can assume from the diagram that the sum of all of these angles equals a straight angle, or 180 degrees.
Thus, 180 = 90 + 56 + x. When this equation is solved, x = 34.
Therefore, the answer to #4 is a. x = 34