document.write( "Question 418055: In triangle ABC, the measure of B is 2 degrees more than three times the measure of angle A. The measure of angle C is 43 degrees more than the measure of angle A. Find the answer for each angle. \n" ); document.write( "

Algebra.Com's Answer #292662 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Start with:
\n" ); document.write( "1) A+B+C = 180 In any triangle, the sum of the interior angles is 180 degrees.
\n" ); document.write( "2) B = 3A+2 \"...the measure of B is 2 degrees more than three times the measure of angle A.\"
\n" ); document.write( "3) C = A+43 \"The measure of angle C is 43 degrees more than the measure of angle A.\"
\n" ); document.write( "Substitute equations 2) and 3) into equation 1).
\n" ); document.write( "1a) A+(3A+2)+(A+43) = 180 Simplify.
\n" ); document.write( "5A+45 = 180 Subtract 45 from both sides.
\n" ); document.write( "5A = 135 Divide both sides by 5.
\n" ); document.write( "A = 27
\n" ); document.write( "B = 3(27)+2
\n" ); document.write( "B = 83
\n" ); document.write( "C = 27+43
\n" ); document.write( "C = 70
\n" ); document.write( "The measure of angle A is 27 degrees.
\n" ); document.write( "The measure of angle B is 83 degrees.
\n" ); document.write( "The measure of angle C is 70 degrees.
\n" ); document.write( "Check:
\n" ); document.write( "A+B+C = 22+83+70 = 180 \n" ); document.write( "

\n" );