SOLUTION: If two angles are complementary, the sum of their angle measures equals 90 degrees. The measure of the two complementary angles are 7x + 17 and 3x - 22. What are the measures of th

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Question 1057253: If two angles are complementary, the sum of their angle measures equals 90 degrees. The measure of the two complementary angles are 7x + 17 and 3x - 22. What are the measures of the two angles?
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
Since the sum of the angles must be 90 degrees, you can write the following equation:

(7x + 17) + (3x - 22) = 90

Collecting and combining like terms on the left gives:

10x - 5 = 90

Adding 5 to both sides then gives:

10x = 95

And dividing both sides by 10 leaves:

x = 9.5

Now, substitute x = 9.5 into the expression for each angle:

First angle: 7(9.5) + 17 = 83.5 degrees

Second angle: 3(9.5) - 22 = 6.5 degrees

As a check, add the angles together and make sure that the sum is 90:

83.5 + 6.5 = 90

90 = 90

so the solution checks.