Final answer:
To find the measures of two complementary angles (∠J and ∠K), set up an equation. Solve the equation to find the measures of ∠K and ∠J.
Step-by-step explanation:
To find the measures of two complementary angles (∠J and ∠K), we can set up an equation using the given information. Let's assume the measure of ∠K is x. According to the problem, ∠J is 9 less than twice the measure of ∠K, so we can write this as ∠J = 2x - 9.
Since the angles are complementary, their measures should add up to 90 degrees. Therefore, we can set up the equation ∠J + ∠K = 90. Substituting the value of ∠J from the first equation, we have (2x - 9) + x = 90. Solving this equation, we get 3x - 9 = 90, which simplifies to 3x = 99. Dividing both sides by 3, we find that x = 33.
So, ∠K = 33 degrees and ∠J = 2(33) - 9 = 57 degrees.