document.write( "Question 1120157: The largest angle in a triangle is twice the degree measure of the second largest angle. one-third of the largest angle is 10 degrees larger than the difference of the other two. What is the measure in degrees of the smallest angle? \n" ); document.write( "

Algebra.Com's Answer #735825 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!
The largest angle in a triangle is twice the degree measure of the second largest angle. one-third of the largest angle is 10 degrees larger than the difference of the other two. What is the measure in degrees of the smallest angle?
\n" ); document.write( "

Let measures of smallest, middle, and largest angles be S, M, and L, respectively
\n" );
document.write( "Then L = 2M ------ eq (i)
\n" );
document.write( "Also,  
\n" );
document.write( "L = 3M - 3S + 30 --------- Multiplying by LCD, 3
\n" );
document.write( "2M = 3M - 3S + 30 -------- Replacing L with 2M
\n" );
document.write( "3S - 30 = M ------- eq (ii)
\n" );
document.write( "In addition, S + M + L = 180______S + M + 2M = 180______S + 3M = 180 ------ eq (iii)
\n" );
document.write( "S + 3(3S - 30) = 180 ------- Replacing M with 3S - 30 in eq (iii)
\n" );
document.write( "S + 9S - 90 = 180
\n" );
document.write( "10S = 270
\n" );
document.write( "S, or measure of smallest angle =  \n" );
document.write( "

\n" );