SOLUTION: The supplement of an angle exceeds five times the complement of an angle by 10 degrees. Find the angle.

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Question 218082: The supplement of an angle exceeds five times the complement of an angle by 10 degrees. Find the angle.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The supplement of an angle exceeds five times the complement of an angle by 10 degrees. Find the angle.

Step 1. Complementary angles is when two angles add up to 90 degrees.

Step 2. Supplementary angles is when two angles add up to 180 degrees.

Step 3. Let x be the angle.

Step 4. Let 90-x its complementary angle.

Step 5. Let 180-x be its supplementary angle.

Step 6. Let 5(90-x) be five times the complement

Step 7. 180-x=5(90-x)+10 since the supplement of an angle exceeds five times the complement of an angle by 10 degrees. Find the angle.

Step 8. Solving yields the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: x=70.
  • Graphical form: Equation 180-x=5%2A%2890-x%29%2B10 was fully solved.
  • Text form: 180-x=5*(90-x)+10 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+180-x=5%2A%2890-x%29%2B10+%29
    For tutors: simplify_cartoon( 180-x=5*(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=5%2A%2890-x%29%2B10.
Moved 180 to the right of expression
It becomes -x%2Bhighlight_green%28+180+%29=5%2A%2890-x%29%2B10.
Look at -x%2B180=5%2A%28highlight_red%28+90+%29-x%29%2B10.
Moved 90 to the right of expression
It becomes -x%2B180=5%2A%28-x%2Bhighlight_green%28+90+%29%29%2B10.
Look at -x%2B180=highlight_red%28+5%2A%28-x%2B90%29%2B10+%29.
Moved these terms to the left highlight_green%28+-5%2A%28-x%2B90%29+%29,highlight_green%28+-10+%29
It becomes -x%2B180-highlight_green%28+5%2A%28-x%2B90%29+%29-highlight_green%28+10+%29=0.
Look at -x%2Bhighlight_red%28+180+%29-5%2A%28-x%2B90%29-highlight_red%28+10+%29=0.
Added fractions or integers together
It becomes -x%2Bhighlight_green%28+170+%29-5%2A%28-x%2B90%29=0.
Look at -x%2Bhighlight_red%28+170+%29-5%2A%28-x%2B90%29=0.
Moved 170 to the right of expression
It becomes -x-5%2A%28-x%2B90%29%2Bhighlight_green%28+170+%29=0.
Look at -x-highlight_red%28+5%2A%28-x%2B90%29+%29%2B170=0.
Expanded term -5 by using associative property on %28-x%2B90%29
It becomes -x%2Bhighlight_green%28+5%2Ax+%29-highlight_green%28+5%2A90+%29%2B170=0.
Look at -x%2B5%2Ax-highlight_red%28+5+%29%2Ahighlight_red%28+90+%29%2B170=0.
Multiplied numerator integers
It becomes -x%2B5%2Ax-highlight_green%28+450+%29%2B170=0.
Look at -x%2B5%2Ax-highlight_red%28+450+%29%2Bhighlight_red%28+170+%29=0.
Added fractions or integers together
It becomes -x%2B5%2Ax%2Bhighlight_green%28+-280+%29=0.
Look at -x%2B5%2Ax%2Bhighlight_red%28+-280+%29=0.
Removed extra sign in front of -280
It becomes -x%2B5%2Ax-highlight_green%28+280+%29=0.
Look at -highlight_red%28+x+%29%2Bhighlight_red%28+5%2Ax+%29-280=0.
Eliminated similar terms highlight_red%28+-x+%29,highlight_red%28+5%2Ax+%29 replacing them with highlight_green%28+%28-1%2B5%29%2Ax+%29
It becomes highlight_green%28+%28-1%2B5%29%2Ax+%29-280=0.
Look at %28-highlight_red%28+1+%29%2Bhighlight_red%28+5+%29%29%2Ax-280=0.
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2Ax-280=0.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2Ax+%29-280=0.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2Ax-280=0.
Look at highlight_red%28+4%2Ax-280+%29=0.
Solved linear equation highlight_red%28+4%2Ax-280=0+%29 equivalent to 4*x-280 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=70.

Universal Simplifier and Solver


Done!



With x=70, then 90-x=20 and 180-x=110.

Check...180-x=5(90-x)+10 or 110=5*20+10=110...which is a true statement.

Step 9. ANSWER: The angle is 70 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