SOLUTION: "find the measure of an angle if five times the measure of its complement is 24 less than twice the measure of its supplement" what would the equation be for this?...

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Question 217425: "find the measure of an angle if five times the measure of its complement is 24 less than twice the measure of its supplement" what would the equation be for this?...
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
"Find the measure of an angle if five times the measure of its complement is 24 less than twice the measure of its supplement" what would the equation be for this?...

Step 1. Two angles are complementary when they add up to 90 degrees and two angles are supplementary when they add up to 180 degrees

Step 2. Let x be the angle.

Step 3. Let 90-x be the complementary angle.

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

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

Step 6. Let 2(180-x) be twice the measure of its supplement

Step 7. Let 5(90-x)=2(180-x)-24 since five times the measure of its complement is 24 less than twice the measure of its supplement
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Step 8. Then solving the equation of Step 7 5%28x-90%29=2%28180-x%29-24 will lead to the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: x=38.
  • Graphical form: Equation 5%2A%2890-x%29=2%2A%28180-x%29-24 was fully solved.
  • Text form: 5*(90-x)=2*(180-x)-24 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5%2A%2890-x%29=2%2A%28180-x%29-24+%29
    For tutors: simplify_cartoon( 5*(90-x)=2*(180-x)-24 )
  • 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%29-24.
Moved 90 to the right of expression
It becomes 5%2A%28-x%2Bhighlight_green%28+90+%29%29=2%2A%28180-x%29-24.
Look at 5%2A%28-x%2B90%29=2%2A%28highlight_red%28+180+%29-x%29-24.
Moved 180 to the right of expression
It becomes 5%2A%28-x%2B90%29=2%2A%28-x%2Bhighlight_green%28+180+%29%29-24.
Look at 5%2A%28-x%2B90%29=highlight_red%28+2%2A%28-x%2B180%29-24+%29.
Moved these terms to the left highlight_green%28+-2%2A%28-x%2B180%29+%29,highlight_green%28+24+%29
It becomes 5%2A%28-x%2B90%29-highlight_green%28+2%2A%28-x%2B180%29+%29%2Bhighlight_green%28+24+%29=0.
Look at highlight_red%28+5%2A%28-x%2B90%29+%29-2%2A%28-x%2B180%29%2B24=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%2B24=0.
Look at -5%2Ax%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+90+%29-2%2A%28-x%2B180%29%2B24=0.
Multiplied numerator integers
It becomes -5%2Ax%2Bhighlight_green%28+450+%29-2%2A%28-x%2B180%29%2B24=0.
Look at -5%2Ax%2Bhighlight_red%28+450+%29-2%2A%28-x%2B180%29%2Bhighlight_red%28+24+%29=0.
Added fractions or integers together
It becomes -5%2Ax%2Bhighlight_green%28+474+%29-2%2A%28-x%2B180%29=0.
Look at -5%2Ax%2Bhighlight_red%28+474+%29-2%2A%28-x%2B180%29=0.
Moved 474 to the right of expression
It becomes -5%2Ax-2%2A%28-x%2B180%29%2Bhighlight_green%28+474+%29=0.
Look at -5%2Ax-highlight_red%28+2%2A%28-x%2B180%29+%29%2B474=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%2B474=0.
Look at -5%2Ax%2B2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+180+%29%2B474=0.
Multiplied numerator integers
It becomes -5%2Ax%2B2%2Ax-highlight_green%28+360+%29%2B474=0.
Look at -5%2Ax%2B2%2Ax-highlight_red%28+360+%29%2Bhighlight_red%28+474+%29=0.
Added fractions or integers together
It becomes -5%2Ax%2B2%2Ax%2Bhighlight_green%28+114+%29=0.
Look at -highlight_red%28+5%2Ax+%29%2Bhighlight_red%28+2%2Ax+%29%2B114=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%2B114=0.
Look at %28-highlight_red%28+5+%29%2Bhighlight_red%28+2+%29%29%2Ax%2B114=0.
Added fractions or integers together
It becomes %28highlight_green%28+-3+%29%29%2Ax%2B114=0.
Look at %28highlight_red%28+-3+%29%29%2Ax%2B114=0.
Removed extra sign in front of -3
It becomes %28-highlight_green%28+3+%29%29%2Ax%2B114=0.
Look at highlight_red%28+%28-highlight_red%28+3+%29%29%2Ax+%29%2B114=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes -highlight_green%28+3+%29%2Ax%2B114=0.
Look at highlight_red%28+-3%2Ax%2B114+%29=0.
Solved linear equation highlight_red%28+-3%2Ax%2B114=0+%29 equivalent to -3*x+114 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=38.

Universal Simplifier and Solver


Done!



So x=38 and 90-x=52 and 180-x=142.

Check...5%28x-90%29=2%28x-180%29-24 if true...5*52=2*142-24...which is a true statement.

Step 9. ANSWER: The angle is 38 degrees, its complementary angle is 52 degrees and its supplementary angle is 142 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