SOLUTION: The measure of the supplement of an angle exceeds 3 times the measure of the complement of the angle by 10. Find the measure of the complement.

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Question 214265: The measure of the supplement of an angle exceeds 3 times the measure of the complement of the angle by 10. Find the measure of the complement.
Answer by drj(1380) About Me  (Show Source):
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The measure of the supplement of an angle exceeds 3 times the measure of the complement of the angle by 10. Find the measure of the complement.

Step 1. Supplementary angles is when two angles add up to 180 degrees and complementary angles is when two angles add up to 90 degrees.

Step 2. Let x be the angle, 90-x be its complement, and 180-x be its supplement.

Step 3. 3(90-x) 3 times the complement.

Step 4. 180-x=3(90-x)+10 The measure of the supplement of an angle exceeds 3 times the measure of the complement of the angle by 10.

Step 5. The following steps will solve the above equation in Step 3.

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


YOUR ANSWER


  • This is an equation! Solutions: x=50.
  • Graphical form: Equation 180-x=3%2A%2890-x%29%2B10 was fully solved.
  • Text form: 180-x=3*(90-x)+10 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+180-x=3%2A%2890-x%29%2B10+%29
    For tutors: simplify_cartoon( 180-x=3*(90-x)+10 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+180+%29-x=3%2A%2890-x%29%2B10.
Moved 180 to the right of expression
It becomes -x%2Bhighlight_green%28+180+%29=3%2A%2890-x%29%2B10.
Look at -x%2B180=3%2A%28highlight_red%28+90+%29-x%29%2B10.
Moved 90 to the right of expression
It becomes -x%2B180=3%2A%28-x%2Bhighlight_green%28+90+%29%29%2B10.
Look at -x%2B180=highlight_red%28+3%2A%28-x%2B90%29%2B10+%29.
Moved these terms to the left highlight_green%28+-3%2A%28-x%2B90%29+%29,highlight_green%28+-10+%29
It becomes -x%2B180-highlight_green%28+3%2A%28-x%2B90%29+%29-highlight_green%28+10+%29=0.
Look at -x%2Bhighlight_red%28+180+%29-3%2A%28-x%2B90%29-highlight_red%28+10+%29=0.
Added fractions or integers together
It becomes -x%2Bhighlight_green%28+170+%29-3%2A%28-x%2B90%29=0.
Look at -x%2Bhighlight_red%28+170+%29-3%2A%28-x%2B90%29=0.
Moved 170 to the right of expression
It becomes -x-3%2A%28-x%2B90%29%2Bhighlight_green%28+170+%29=0.
Look at -x-highlight_red%28+3%2A%28-x%2B90%29+%29%2B170=0.
Expanded term -3 by using associative property on %28-x%2B90%29
It becomes -x%2Bhighlight_green%28+3%2Ax+%29-highlight_green%28+3%2A90+%29%2B170=0.
Look at -x%2B3%2Ax-highlight_red%28+3+%29%2Ahighlight_red%28+90+%29%2B170=0.
Multiplied numerator integers
It becomes -x%2B3%2Ax-highlight_green%28+270+%29%2B170=0.
Look at -x%2B3%2Ax-highlight_red%28+270+%29%2Bhighlight_red%28+170+%29=0.
Added fractions or integers together
It becomes -x%2B3%2Ax%2Bhighlight_green%28+-100+%29=0.
Look at -x%2B3%2Ax%2Bhighlight_red%28+-100+%29=0.
Removed extra sign in front of -100
It becomes -x%2B3%2Ax-highlight_green%28+100+%29=0.
Look at -highlight_red%28+x+%29%2Bhighlight_red%28+3%2Ax+%29-100=0.
Eliminated similar terms highlight_red%28+-x+%29,highlight_red%28+3%2Ax+%29 replacing them with highlight_green%28+%28-1%2B3%29%2Ax+%29
It becomes highlight_green%28+%28-1%2B3%29%2Ax+%29-100=0.
Look at %28-highlight_red%28+1+%29%2Bhighlight_red%28+3+%29%29%2Ax-100=0.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2Ax-100=0.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2Ax+%29-100=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2Ax-100=0.
Look at highlight_red%28+2%2Ax-100+%29=0.
Solved linear equation highlight_red%28+2%2Ax-100=0+%29 equivalent to 2*x-100 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=50.

Universal Simplifier and Solver


Done!



Step 6. The complement of x=50 degrees is 90-x=40 degrees.

Step 7. ANSWER: The complement of the angle is 40 degrees.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction 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