The measure of an angle is forty-four times the measure of a complementary angle. what is the measure of each angle?

In geometry, complementary angles are at least a group of two angles that sum up to 90° or a right angle. So, suppose the two unknown complementary angles are α and β. Then,

α + β = 90°

Since there are two unknowns, we nee two independent equations as well. Thus, we need another equation to solve the system. That comes from the relationship between α and β. Suppose α is greater than β. Then,

α = 44*β

Substituting this to the first equation,

44β + β = 90
45β = 90
β = 2°

Then, knowing that β is 2°,
α = 90 - 2 = 88°

Therefore, the complementary angles are 2° and 88°.