Final answer:
The size of angle x is 126 degrees and the angle fact used is 54. Angle x and angle y are both equal to 54 degrees.
Step-by-step explanation:
For part (a), the size of angle x can be found using the provided information. The angle fact 54 shows that angle x and angle y are supplementary angles, which means they add up to 180 degrees. Therefore, if angle y is 54 degrees, angle x must be 180 - 54 = 126 degrees.
For part (b), the angle fact that shows angle x and angle y are equal is 54. Since the angles x and y are supplementary, if angle x is 54 degrees, then angle y must also be 54 degrees.