SOLUTION: Five times the complement of an angle less twice the angle's supplement is 40 degrees. Find the measure of the supplement.

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Question 215898: Five times the complement of an angle less twice the angle's supplement is 40 degrees. Find the measure of the supplement.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Five times the complement of an angle less twice the angle's supplement is 40 degrees. Find the measure of the supplement.

Step 1. Complementary angles means two angles add up to 90 degrees.

Step 2. Supplementary angles means two angles add up to 180 degrees.

Step 3. Let x be the angle, let 90-x be its complement, let 180-x be its supplement.

Step 4. Let 5(90-x) be five times the complement and 2(180-x) be twice the supplement.

Step 5. Five times the complement of an angle less twice the angle's supplement is 40 degrees is translated as

5%2890-x%29-2%28180-x%29=40

The following will solve this equation...

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


YOUR ANSWER


  • This is an equation! Solutions: x=16.6666666666667.
  • Graphical form: Equation 5%2A%2890-x%29-2%2A%28180-x%29=40 was fully solved.
  • Text form: 5*(90-x)-2*(180-x)=40 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5%2A%2890-x%29-2%2A%28180-x%29=40+%29
    For tutors: simplify_cartoon( 5*(90-x)-2*(180-x)=40 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2A%28highlight_red%28+90+%29-x%29-2%2A%28180-x%29=40.
Moved 90 to the right of expression
It becomes 5%2A%28-x%2Bhighlight_green%28+90+%29%29-2%2A%28180-x%29=40.
Look at 5%2A%28-x%2B90%29-2%2A%28highlight_red%28+180+%29-x%29=40.
Moved 180 to the right of expression
It becomes 5%2A%28-x%2B90%29-2%2A%28-x%2Bhighlight_green%28+180+%29%29=40.
Look at 5%2A%28-x%2B90%29-2%2A%28-x%2B180%29=highlight_red%28+40+%29.
Moved these terms to the left highlight_green%28+-40+%29
It becomes 5%2A%28-x%2B90%29-2%2A%28-x%2B180%29-highlight_green%28+40+%29=0.
Look at highlight_red%28+5%2A%28-x%2B90%29+%29-2%2A%28-x%2B180%29-40=0.
Expanded term 5 by using associative property on %28-x%2B90%29
It becomes -highlight_green%28+5%2Ax+%29%2Bhighlight_green%28+5%2A90+%29-2%2A%28-x%2B180%29-40=0.
Look at -5%2Ax%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+90+%29-2%2A%28-x%2B180%29-40=0.
Multiplied numerator integers
It becomes -5%2Ax%2Bhighlight_green%28+450+%29-2%2A%28-x%2B180%29-40=0.
Look at -5%2Ax%2Bhighlight_red%28+450+%29-2%2A%28-x%2B180%29-highlight_red%28+40+%29=0.
Added fractions or integers together
It becomes -5%2Ax%2Bhighlight_green%28+410+%29-2%2A%28-x%2B180%29=0.
Look at -5%2Ax%2Bhighlight_red%28+410+%29-2%2A%28-x%2B180%29=0.
Moved 410 to the right of expression
It becomes -5%2Ax-2%2A%28-x%2B180%29%2Bhighlight_green%28+410+%29=0.
Look at -5%2Ax-highlight_red%28+2%2A%28-x%2B180%29+%29%2B410=0.
Expanded term -2 by using associative property on %28-x%2B180%29
It becomes -5%2Ax%2Bhighlight_green%28+2%2Ax+%29-highlight_green%28+2%2A180+%29%2B410=0.
Look at -5%2Ax%2B2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+180+%29%2B410=0.
Multiplied numerator integers
It becomes -5%2Ax%2B2%2Ax-highlight_green%28+360+%29%2B410=0.
Look at -5%2Ax%2B2%2Ax-highlight_red%28+360+%29%2Bhighlight_red%28+410+%29=0.
Added fractions or integers together
It becomes -5%2Ax%2B2%2Ax%2Bhighlight_green%28+50+%29=0.
Look at -highlight_red%28+5%2Ax+%29%2Bhighlight_red%28+2%2Ax+%29%2B50=0.
Eliminated similar terms highlight_red%28+-5%2Ax+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%28-5%2B2%29%2Ax+%29
It becomes highlight_green%28+%28-5%2B2%29%2Ax+%29%2B50=0.
Look at %28-highlight_red%28+5+%29%2Bhighlight_red%28+2+%29%29%2Ax%2B50=0.
Added fractions or integers together
It becomes %28highlight_green%28+-3+%29%29%2Ax%2B50=0.
Look at %28highlight_red%28+-3+%29%29%2Ax%2B50=0.
Removed extra sign in front of -3
It becomes %28-highlight_green%28+3+%29%29%2Ax%2B50=0.
Look at highlight_red%28+%28-highlight_red%28+3+%29%29%2Ax+%29%2B50=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes -highlight_green%28+3+%29%2Ax%2B50=0.
Look at highlight_red%28+-3%2Ax%2B50+%29=0.
Solved linear equation highlight_red%28+-3%2Ax%2B50=0+%29 equivalent to -3*x+50 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=16.6666666666667.

Universal Simplifier and Solver


Done!



With x=16.67, then 180-x=163.33 and 90-x=73.33

Step 6. ANSWER. The supplement is 163.33 degrees

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