What is the measure of angles in a right triangle besides the right angle?

In a right triangle, one angle measures exactly 90 degrees, which is the definition of a right angle. The other two angles must be such that their measures add up to 90 degrees as well. This is because the sum of all angles in any triangle is always 180 degrees.

Since one angle is already occupied by the right angle, the remaining two angles must be acute. An acute angle is defined as an angle that measures less than 90 degrees. Therefore, both of the other angles in a right triangle must be acute angles, ensuring that their combined measure together with the right angle sums to exactly 180 degrees. This fundamental property of triangles restricts the other angles in a right triangle to be acute, making this the correct choice.