SOLUTION: The measure of the complement of an angle is 3x+9. The measure of the supplement of an angle is 3x+99. What is the measure of the angle?

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Question 213114: The measure of the complement of an angle is 3x+9. The measure of the supplement of an angle is 3x+99. What is the measure of the angle?
Answer by drj(1380) About Me  (Show Source):
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The measure of the complement of an angle is 3x+9. The measure of the supplement of an angle is 3x+99. What is the measure of the angle?

Step 1. The complement is when two angles add up to 90 degrees and the supplement is when the two angles add up to 180 degrees.

Step 2. let x be the measure of the unknown angle.

Step 3. Let 90 -x be its complement and 180- x be the supplement of the angle.

Step 4. Given 90-x=3x+9 The measure of the complement of an angle is 3x+9. Solve using the following steps.

90-x=3x%2B9
Add x-9 to both sides to isolate x-terms on right side and numbers on left.

90-x%2Bx-9=3x%2B9%2Bx-9

90-x%2Bx-9=3x%2B9%2Bx-9

91=4x

Divide by 4 to both sides yields

91%2F4=x

Step 5. Given 3x+99=180-x. The measure of the supplement of an angle is 3x+99. So

3x%2B99=180-x

Add x+99 to both sides of equation to isolate x on right side and numbers on left

3x%2B99%2Bx-99=180-x%2Bx-99

4x=91

x=91%2F4

Step 6. The angle is x=91%2F4.


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J