SOLUTION: Find the measure of an angle if five times the measure of its complement is 24 degrees less than twice the measure of its supplement. This is what I have: 5 (90-x)=2 (180-x)-24

Question 907108: Find the measure of an angle if five times the measure of its complement is 24 degrees less than twice the measure of its supplement.
This is what I have: 5 (90-x)=2 (180-x)-24 but I can't get a positive answer. Can you help?
Found 2 solutions by richwmiller, MathLover1:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
5 (90-x)=2 (180-x)-24
450-5x=360=2s-24
90=3x-24
114=3x
x=38

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Step 1. Two angles are complementary when they add up to degrees and two angles are supplementary when they add up to degrees

Step 2. Let be the angle.

Step 3. Let be the complementary angle.

Step 4. Let be the supplementary angle.

Step 5. Let be five times the complement of the angle.

Step 6. Let be twice the measure of its supplement

Step 7. Let since five times the measure of its complement is less than twice the measure of its supplement
)
Step 8. Then solving the equation of Step 7 will lead to the following steps:

....solve for

So and and .

Check... if true than => which is a true statement.

ANSWER:
The angle is degrees, its complementary angle is degrees and its supplementary angle is degrees.

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