SOLUTION: can you please help me figure out the supplement of a given angle is four times as large as a complement of the angle. Find the measure of the given angle. Please.

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Question 224936: can you please help me figure out the supplement of a given angle is four times as large as a complement of the angle. Find the measure of the given angle. Please.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Can you please help me figure out the supplement of a given angle is four times as large as a complement of the angle. Find the measure of the given angle. Please.

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.

Step 4. Let 180-x be its supplementary angle.

Step 5. Let 90-x be its complementary angle.

Step 6. Then 180-x=4(90-x) since the supplement of a given angle is four times as large as a complement of the angle

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=60.
  • Graphical form: Equation 180-x=4%2A%2890-x%29 was fully solved.
  • Text form: 180-x=4*(90-x) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+180-x=4%2A%2890-x%29+%29
    For tutors: simplify_cartoon( 180-x=4*(90-x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+180+%29-x=4%2A%2890-x%29.
Moved 180 to the right of expression
It becomes -x%2Bhighlight_green%28+180+%29=4%2A%2890-x%29.
Look at -x%2B180=4%2A%28highlight_red%28+90+%29-x%29.
Moved 90 to the right of expression
It becomes -x%2B180=4%2A%28-x%2Bhighlight_green%28+90+%29%29.
Look at -x%2B180=highlight_red%28+4%2A%28-x%2B90%29+%29.
Moved these terms to the left highlight_green%28+-4%2A%28-x%2B90%29+%29
It becomes -x%2B180-highlight_green%28+4%2A%28-x%2B90%29+%29=0.
Look at -x%2Bhighlight_red%28+180+%29-4%2A%28-x%2B90%29=0.
Moved 180 to the right of expression
It becomes -x-4%2A%28-x%2B90%29%2Bhighlight_green%28+180+%29=0.
Look at -x-highlight_red%28+4%2A%28-x%2B90%29+%29%2B180=0.
Expanded term -4 by using associative property on %28-x%2B90%29
It becomes -x%2Bhighlight_green%28+4%2Ax+%29-highlight_green%28+4%2A90+%29%2B180=0.
Look at -x%2B4%2Ax-highlight_red%28+4+%29%2Ahighlight_red%28+90+%29%2B180=0.
Multiplied numerator integers
It becomes -x%2B4%2Ax-highlight_green%28+360+%29%2B180=0.
Look at -x%2B4%2Ax-highlight_red%28+360+%29%2Bhighlight_red%28+180+%29=0.
Added fractions or integers together
It becomes -x%2B4%2Ax%2Bhighlight_green%28+-180+%29=0.
Look at -x%2B4%2Ax%2Bhighlight_red%28+-180+%29=0.
Removed extra sign in front of -180
It becomes -x%2B4%2Ax-highlight_green%28+180+%29=0.
Look at -highlight_red%28+x+%29%2Bhighlight_red%28+4%2Ax+%29-180=0.
Eliminated similar terms highlight_red%28+-x+%29,highlight_red%28+4%2Ax+%29 replacing them with highlight_green%28+%28-1%2B4%29%2Ax+%29
It becomes highlight_green%28+%28-1%2B4%29%2Ax+%29-180=0.
Look at %28-highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%29%2Ax-180=0.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ax-180=0.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-180=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ax-180=0.
Look at highlight_red%28+3%2Ax-180+%29=0.
Solved linear equation highlight_red%28+3%2Ax-180=0+%29 equivalent to 3*x-180 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=60.

Universal Simplifier and Solver


Done!



With x=60, then 180-x-120 and 90-60=30 and note that four times the complement of the angle is the supplement of the angle.

Step 7. ANSWER: The angle is 60 degrees. It complement is 30 degrees and its supplement is 120 degrees.

I hope the above steps were helpful.

For free Step-By-Step Videos on Intrduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
drjctu@gmail.com
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