Final answer:
The larger angle measures 79° and the smaller angle measures 11°.
Step-by-step explanation:
To find the measures of the two angles, let's assume that the larger angle is represented by x° and the smaller angle is represented by (90° - x°), as the angles are complementary. According to the given information, the difference between the measures of the two angles is 68°. So we can set up the equation: x° - (90° - x°) = 68°. Solving this equation gives us x = 79°. Therefore, the larger angle is 79° and the smaller angle is (90° - 79°) = 11°.