To find the measure of angle A' after rotating triangle ABC 45 degrees clockwise about the origin, we start with angle A, which measures 78 degrees.
When we rotate a triangle, the angles themselves do not change; only their positions in the coordinate plane are altered. Therefore, the measure of angle A' will remain the same as that of angle A.
Thus, angle A' also measures 78 degrees.
So, the correct answer is: 78o