Angle ABC is given to be 90 degrees. By the converse of Thales Theorem, we know that AC is a diameter of the circle. If we draw a line from A to C, it will pass through the center of the circle.
Therefore, arc AC is 180 degrees as this is half the distance around the circle.
minor arc AD = 72 minor arc CD = x (minor arc AD) + (minor arc CD) = arc AC 72+x = 180 72+x-72 = 180-72 x = 108
