Quantitative Literacy Practice Exam

To determine the measures of the two complementary angles, we need to start with the definition of complementary angles, which states that two angles add up to 90 degrees. In this scenario, we have the expressions for the angles as (13z + 5)° and (20z - 14)°. The equation to set up based on their complementary nature is: (13z + 5) + (20z - 14) = 90. Combining the terms gives: 33z - 9 = 90. Next, we reorganize this to solve for z: 33z = 90 + 9, 33z = 99, z = 3. Now that we have the value of z, we can find the measures of the angles by substituting z back into the original angle expressions: For the first angle: 13(3) + 5 = 39 + 5 = 44°. For the second angle: 20(3) - 14 = 60 - 14 = 46°. So the measures of the angles are 44° and 46°. This correctly matches the selection provided, illustrating that the angles not only add up to 90 degrees but are