document.write( "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?... \n" ); document.write( "
Algebra.Com's Answer #163953 by drj(1380)\"\" \"About 
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?...\r
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\n" ); document.write( "\n" ); document.write( "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\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let x be the angle.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 90-x be the complementary angle.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let 180-x be the supplementary angle.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Let 5(90-x) be five times the complement of the angle.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. Let 2(180-x) be twice the measure of its supplement\r
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\n" ); document.write( "\n" ); document.write( "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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\n" ); document.write( "\n" ); document.write( "Step 8. Then solving the equation of Step 7 \"5%28x-90%29=2%28180-x%29-24\" will lead to the following steps:\r
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • This is an equation! Solutions: x=38.
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  • 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 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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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\".
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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\".
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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\".
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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\".
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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\".
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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\".
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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\".
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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\".
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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\".
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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\".
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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\".
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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\".
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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\".
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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\".
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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\"
\n" ); document.write( "This is an equation! Solutions: x=38.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "So x=38 and 90-x=52 and 180-x=142.\r
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\n" ); document.write( "\n" ); document.write( "Check...\"5%28x-90%29=2%28x-180%29-24\" if true...5*52=2*142-24...which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 9. ANSWER: The angle is 38 degrees, its complementary angle is 52 degrees and its supplementary angle is 142 degrees\r
\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful. \r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "And good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J\r
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