document.write( "Question 1152598: The sum of the measures of the angles of the triangle is 180.The sum of the measure of the second and third angles is 5 times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and z represent the measure of the first, second and third angles respectively. Find the measure of the 3 angles. \n" ); document.write( "
Algebra.Com's Answer #774645 by ankor@dixie-net.com(22740)\"\" \"About 
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Write an equation for each statement
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\n" ); document.write( "The sum of the measures of the angles of the triangle is 180.
\n" ); document.write( " x + y + z = 180
\n" ); document.write( ":
\n" ); document.write( "The sum of the measure of the second and third angles is 5 times the measure of the first angle.
\n" ); document.write( " 5(y+z) = x
\n" ); document.write( "5y + 5z = x
\n" ); document.write( "-x + 5y + 5z = 0
\n" ); document.write( ":
\n" ); document.write( "The third angle is 16 more than the second.
\n" ); document.write( " z = y + 16
\n" ); document.write( "-y + z = 16
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 5, subtract the 2nd (rearranged equation)
\n" ); document.write( "5x + 5y + 5z = 900
\n" ); document.write( "-x + 5y + 5z = 0
\n" ); document.write( "---------------------Subtraction eliminates y and z, find z
\n" ); document.write( "6x + 0 + 0 = 900
\n" ); document.write( "x = 900/6
\n" ); document.write( "x = 150 degrees
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\n" ); document.write( "Therefore we know y + z = 30 degrees
\n" ); document.write( "using this and the last equation
\n" ); document.write( "y + z = 30
\n" ); document.write( "-y+ z = 16
\n" ); document.write( "--------------Addition eliminates y, find z
\n" ); document.write( "0 + 2z = 46
\n" ); document.write( "z = 46/2
\n" ); document.write( "z = 23 degrees
\n" ); document.write( ":
\n" ); document.write( "Find y
\n" ); document.write( "150 + y + 23 = 180
\n" ); document.write( "y = 180 - 173
\n" ); document.write( "y = 7 degrees
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\n" ); document.write( "Check this in the statement
\n" ); document.write( "\"The sum of the measure of the second and third angles is 5 times the measure of the first angle.\"
\n" ); document.write( "5(7 + 23) = 150
\n" ); document.write( "5(30) = 150\r
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