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Given h and k are complementary angles such that h> k. If the difference between h and k is 24° calculate the values of h and k.​

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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.

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