SOLUTION: One third of the supplement of an angle added to the complement of an angle is 86. Find the measure of the angle, its complement, and its supplement. Any help provided, preferab

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Question 215826: One third of the supplement of an angle added to the complement of an angle is 86. Find the measure of the angle, its complement, and its supplement.
Any help provided, preferably with steps, would be immensely appreciated. Much thanks in advance!
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
One third of the supplement of an angle added to the complement of an angle is 86. Find the measure of the angle, its complement, and its supplement.

Step 1. Supplementary angles means two angles add up to 180 degrees.

Step 2. Complementary angles means two angles add up to 90 degrees.

Step 3. Let x be the angle, let 180-x be its supplementary angle, and let 90-x be its complementary angle.

Step 4. Let %28180-x%29%2F3 be one third of the supplementary angle.

Step 5. Then the statement one third of the supplement of an angle added to the complement of an angle is 86 and translated as

%28180-x%29%2F3%2B90-x=86

Multiplying 3 to both sides of the equations to get rid of the denominator

3%2A%28%28180-x%29%2F3%2B90-x%29=3%2A86

180-x%2B270-3x=258

450-4x=258

Add 4x-258 to both sides of the equation to prepare in solving for x

450-4x%2B4x-258=258%2B4x-258

192=4x

Divide by 4 to both sides of the equatiion

192%2F4=4x%2F4

x=48

Then 180-x=132 and 90-x=42

Check...%28180-x%29%2F3%2B90-x=86 if true. Then 132%2F3%2B42=86...which is a true statement.

Step 6. ANSWER. The angle is 42, its supplement is 132, and its complement is 42.

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