document.write( "Question 221642: the measure of the supplement of an angle exceeds three times the measure of the compliment by 30. \n" ); document.write( "

Algebra.Com's Answer #166199 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
The measure of the supplement of an angle exceeds three times the measure of the complement by 30.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Supplementary angles means two angles add up to 180 degrees.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Complementary angles means two angles add up to 90 degrees.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let x be the angle.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let 180-x be its supplementary angle.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Let 90-x be its complementary angle.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. Let 3(90-x) be three times the complement.\r
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\n" ); document.write( "\n" ); document.write( "Step 7. Then 180-x=3(90-x)+30 since the measure of the supplement of an angle exceeds three times the measure of the complement by 30.\r
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\n" ); document.write( "\n" ); document.write( "Step 8. Solving the equation in Step 7 yields the following steps:\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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This is an equation! Solutions: x=60.
Graphical form: Equation $\"180-x=3%2A%2890-x%29%2B30\"$ was fully solved.
Text form: 180-x=3*(90-x)+30 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+180-x=3%2A%2890-x%29%2B30+%29\"$
For tutors: simplify_cartoon( 180-x=3*(90-x)+30 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+180+%29-x=3%2A%2890-x%29%2B30\"$ .
Moved $\"180\"$ to the right of expression
It becomes $\"-x%2Bhighlight_green%28+180+%29=3%2A%2890-x%29%2B30\"$ .
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Look at $\"-x%2B180=3%2A%28highlight_red%28+90+%29-x%29%2B30\"$ .
Moved $\"90\"$ to the right of expression
It becomes $\"-x%2B180=3%2A%28-x%2Bhighlight_green%28+90+%29%29%2B30\"$ .
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Look at $\"-x%2B180=highlight_red%28+3%2A%28-x%2B90%29%2B30+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-3%2A%28-x%2B90%29+%29\"$ , $\"highlight_green%28+-30+%29\"$
It becomes $\"-x%2B180-highlight_green%28+3%2A%28-x%2B90%29+%29-highlight_green%28+30+%29=0\"$ .
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Look at $\"-x%2Bhighlight_red%28+180+%29-3%2A%28-x%2B90%29-highlight_red%28+30+%29=0\"$ .
Added fractions or integers together
It becomes $\"-x%2Bhighlight_green%28+150+%29-3%2A%28-x%2B90%29=0\"$ .
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Look at $\"-x%2Bhighlight_red%28+150+%29-3%2A%28-x%2B90%29=0\"$ .
Moved $\"150\"$ to the right of expression
It becomes $\"-x-3%2A%28-x%2B90%29%2Bhighlight_green%28+150+%29=0\"$ .
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Look at $\"-x-highlight_red%28+3%2A%28-x%2B90%29+%29%2B150=0\"$ .
Expanded term $\"-3\"$ by using associative property on $\"%28-x%2B90%29\"$
It becomes $\"-x%2Bhighlight_green%28+3%2Ax+%29-highlight_green%28+3%2A90+%29%2B150=0\"$ .
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Look at $\"-x%2B3%2Ax-highlight_red%28+3+%29%2Ahighlight_red%28+90+%29%2B150=0\"$ .
Multiplied numerator integers
It becomes $\"-x%2B3%2Ax-highlight_green%28+270+%29%2B150=0\"$ .
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Look at $\"-x%2B3%2Ax-highlight_red%28+270+%29%2Bhighlight_red%28+150+%29=0\"$ .
Added fractions or integers together
It becomes $\"-x%2B3%2Ax%2Bhighlight_green%28+-120+%29=0\"$ .
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Look at $\"-x%2B3%2Ax%2Bhighlight_red%28+-120+%29=0\"$ .
Removed extra sign in front of $\"-120\"$
It becomes $\"-x%2B3%2Ax-highlight_green%28+120+%29=0\"$ .
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Look at $\"-highlight_red%28+x+%29%2Bhighlight_red%28+3%2Ax+%29-120=0\"$ .
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 $\"highlight_green%28+%28-1%2B3%29%2Ax+%29-120=0\"$ .
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Look at $\"%28-highlight_red%28+1+%29%2Bhighlight_red%28+3+%29%29%2Ax-120=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+2+%29%29%2Ax-120=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+2+%29%29%2Ax+%29-120=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$
It becomes $\"highlight_green%28+2+%29%2Ax-120=0\"$ .
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Look at $\"highlight_red%28+2%2Ax-120+%29=0\"$ .
Solved linear equation $\"highlight_red%28+2%2Ax-120=0+%29\"$ equivalent to 2*x-120 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=60.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With x=60, then 180-x=120 and 90-x=30.\r
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\n" ); document.write( "\n" ); document.write( "Check equation 180-x=3(90-x)+30 of Step 7 or 120=3*30+30=120 which is a true statement\r
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\n" ); document.write( "\n" ); document.write( "Step 9. ANSWER: The angle is 60, its supplement is 120 and its complement is 30.\r
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\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 Intrduction 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
\n" ); document.write( "\n" ); document.write( "drjctu@gmail.com\r
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