Explanation:
Let's denote the measure of angle h as "x" and the measure of angle k as "y".
Given that h and k are complementary angles, we know that:
x + y = 90° (Sum of complementary angles is 90°)
We are also given that the difference between h and k is 24°:
x - y = 24°
Now we have a system of two equations with two variables. We can solve this system to find the values of x (h) and y (k).
Adding the two equations together, we get:
(x + y) + (x - y) = 90° + 24°
2x = 114°
Dividing both sides of the equation by 2, we find:
x = 57°
Substituting the value of x into one of the original equations, we find:
57° + y = 90°
y = 90° - 57°
y = 33°
Therefore, the values of h and k are 57° and 33°, respectively.