Answer
(a) The angle of rotation was $180^{\circ}$
(b) The center of this rotation is the center of the circle.
Work Step by Step
(a) At the right angle at point C, the side goes straight up to point B. After rotation, the right angle at point C' points straight down to point A. Therefore, the triangle was rotated $180^{\circ}$
(b) The point of rotation is the midpoint of the line $CC'$. By symmetry, this point is also the midpoint of the line $AB$ which is the center of the circle.
