Final answer:
The measures for angles A and B in a right triangle with the right angle at C must sum up to 90 degrees. Both angles must be acute, meaning they must be greater than 0 degrees and less than 90 degrees.
Step-by-step explanation:
The question involves understanding the geometric properties of a right triangle. In a right triangle, the sum of the angles is always 180 degrees, and since one angle is given as a right angle (90 degrees at point C), the other two angles (A and B) must sum up to 90 degrees. Therefore, the possible measures for angles A and B in triangle ABC must be such that when added together, they equal 90 degrees since angle C is 90 degrees.
For instance, if angle A were 30 degrees, angle B must be 60 degrees, and vice versa. Any other combination of positive angles that add up to 90 degrees would be acceptable. It is essential to keep in mind that both angles must be greater than 0 degrees and less than 90 degrees individually because angles in a triangle cannot be 0 or negative, and since angle C is already 90 degrees, angles A and B must be acute angles.