Find the measure of angle x in the figure below:

Ok here we go, I will go step-by-step:
So first we have to figure out what y is. we see that the angles outside y are 52 and 59, so we add those together and get 111. now we know  whatever y is, it has to equal 180 when added to 111 because it is a straight line. Therefore, angle y is 69 degrees. Now, we also know the angles inside a triangle have to equal 180 when added together. we know two of them. They are 63 and 69. Add those together and we get 132. That means x has to equal 48, to make the inside angles equal 180. The answer is x=48