SOLUTION: the measure of angle b, the supplement of angle a, is four times the measure of angle c, the complement of angle a

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Question 221175: the measure of angle b, the supplement of angle a, is four times the measure of angle c, the complement of angle a
Answer by drj(1380) About Me  (Show Source):
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The measure of angle b, the supplement of angle a, is four times the measure of angle c, the complement 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 b=180-a be the supplement of the angle a.

Step 5. Let c=90-a be the complement of the angle a.

Step 6. Then 180-a= 4(90-a) the measure of angle b, the supplement of angle a, is four times the measure of angle c, the complement of angle a.

Step 7. Simplifying Step 6 yields the following steps:

180-a=+360-4a

Add 4a-180 to both sides of the equation to get variable a in left side and numbers on right side.

180-a%2B4a-180=360-4a%2B4a-180.

3a=180

Divide 3 to both sides of the equation

3a%2F3=180%2F3

a=60 180-a=120 and 90-a=30

Check if equation in Step 6 is true...180-a= 4(90-a) or 120=4*30 which is a true statement.

Step 7. ANSWER: Angle is 60 degrees, its supplementary angle is 120 degrees, and its complementary angle is 30 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