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

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

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) (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.
RELATED QUESTIONS
Recall that two angles are complementary if the sum of their measures 90 degrees. Find... (answered by mananth)

Two angles are complementary if their sum is 90 degrees. If two complementary angles have (answered by drj)

Two angles are complementary if their sum is 90 degrees. If one angle measures x degrees, (answered by Alan3354)

complementary angles. two angles are complementary angles if the sum of their measures is (answered by stanbon)

Two angles are complementary if their sum is 90 degrees. If one angle measures x,... (answered by stanbon,FrankM)

When angles are complementary the sum of their measures is 90 degrees two complementary... (answered by Theo)

Two angles are complementary if the sum of the measures of their angles is 90 degrees.... (answered by solver91311)

Recall that two angles are complementary if the sum of Their measures is 90 degrees.... (answered by josmiceli)

Two angles are complementary if the sum of their measures is 90 degress. If angle A and B (answered by nerdybill)