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Question 221176: the measure of angle b, the complement of angle a, is one-sixth the measurement of angle c, the supplement of angle a
Answer by drj(1380)   (Show Source):
You can put this solution on YOUR website! The measure of angle b, the complement of angle a, is one-sixth the measurement of angle c, the supplement of angle a
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 a be the angle.
Step 4. Let c=180-a be the supplement of the angle a.
Step 5. Let b=90-a be the complement of the angle a.
Step 6. Then 90-a= (180-a)/6 since the measure of angle b, the complement of angle a, is one-sixth the measurement of angle c, the supplement of angle a
Step 7. Simplifying Step 6 yields the following steps:
Multiply by 6 to both sides of the equation to get rid of denominator
Add 6a-180 to both sides of the equation to get variable a in left side and numbers on right side.
 .
Divide 5 to both sides of the equation
  and 
Check if equation in Step 6 is true...90-a= (180-a)/6 or 18=108/6 which is a true statement.
Step 7. ANSWER: Angle is 72 degrees, its supplementary angle is 108 degrees, and its complementary angle is 18 degrees
I hope the above steps and explanation were helpful.
For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.
Respectfully,
Dr J
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