document.write( "Question 836951: one angle of a triangle is four times as large as another the measure of the third angle is 15 degrees more thatn that of the smallest angle find the measure of each angle \n" ); document.write( "
Algebra.Com's Answer #504426 by dfrazzetto(283)\"\" \"About 
You can put this solution on YOUR website!
Set angles a, b, c\r
\n" ); document.write( "\n" ); document.write( "Since all angles must be >0; assume b is smallest angle\r
\n" ); document.write( "\n" ); document.write( "a = 4b
\n" ); document.write( "a + b + c = 180
\n" ); document.write( "c = b + 15\r
\n" ); document.write( "\n" ); document.write( "a + b + c = 180; rewrite in terms of only angle 'b'\r
\n" ); document.write( "\n" ); document.write( "4b + b + b + 15 = 180\r
\n" ); document.write( "\n" ); document.write( "6b + 15 = 180\r
\n" ); document.write( "\n" ); document.write( "b = 27.5 degrees\r
\n" ); document.write( "\n" ); document.write( "a = 4b = 4(27.5) = 110 degrees\r
\n" ); document.write( "\n" ); document.write( "c = b + 15 = 27.5 + 15 = 42.5\r
\n" ); document.write( "\n" ); document.write( "CHECK:\r
\n" ); document.write( "\n" ); document.write( "27.5 + 110 + 42.5 = 180; Correct\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: b=27.5.
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  • Graphical form: Equation \"4b%2Bb%2Bb%2B15=180\" was fully solved.
  • Text form: 4b+b+b+15=180 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+4b%2Bb%2Bb%2B15=180+%29\"
    For tutors: simplify_cartoon( 4b+b+b+15=180 )
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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 \"highlight_red%28+4%2Ab+%29%2Bhighlight_red%28+b+%29%2Bhighlight_red%28+b+%29%2B15=180\".
Eliminated similar terms \"highlight_red%28+4%2Ab+%29\",\"highlight_red%28+b+%29\",\"highlight_red%28+b+%29\" replacing them with \"highlight_green%28+%284%2B1%2B1%29%2Ab+%29\"
It becomes \"highlight_green%28+%284%2B1%2B1%29%2Ab+%29%2B15=180\".
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Look at \"%28highlight_red%28+4+%29%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2Ab%2B15=180\".
Added fractions or integers together
It becomes \"%28highlight_green%28+6+%29%29%2Ab%2B15=180\".
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Look at \"highlight_red%28+%28highlight_red%28+6+%29%29%2Ab+%29%2B15=180\".
Remove unneeded parentheses around factor \"highlight_red%28+6+%29\"
It becomes \"highlight_green%28+6+%29%2Ab%2B15=180\".
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Look at \"6%2Ab%2B15=highlight_red%28+180+%29\".
Moved these terms to the left \"highlight_green%28+-180+%29\"
It becomes \"6%2Ab%2B15-highlight_green%28+180+%29=0\".
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Look at \"6%2Ab%2Bhighlight_red%28+15+%29-highlight_red%28+180+%29=0\".
Added fractions or integers together
It becomes \"6%2Ab%2Bhighlight_green%28+-165+%29=0\".
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Look at \"6%2Ab%2Bhighlight_red%28+-165+%29=0\".
Removed extra sign in front of \"-165\"
It becomes \"6%2Ab-highlight_green%28+165+%29=0\".
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Look at \"highlight_red%28+6%2Ab-165+%29=0\".
Solved linear equation \"highlight_red%28+6%2Ab-165=0+%29\" equivalent to 6*b-165 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: b=27.5.

Universal Simplifier and Solver

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Done!
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