4) angle wpr is equal to angle arp because of alternate interior angles (remember WRAP is a parallelogram)
So:
x + 12 = 2x - 37
49 = x
Now plug in x = 49 for all four angles.
angle ARP = 61
angle WPR = 61
angle WRP = 29
angle APR = 29
So the two corners are both 90 degrees. We can easily see that the other two corners are also 90 degrees, thus this parallelogram is also a rectangle.