document.write( "Question 976589: In a triangle, the second angle is twice the measure of the first, and the third angle is three times the measure of the second. Find the measure of the third angle.
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Algebra.Com's Answer #598253 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! In a triangle, the second angle is twice the measure of the first, and the third angle is three times the measure of the second. Find the measure of the third angle. \n" ); document.write( ": \n" ); document.write( "Three angles, A, B, C. Write an equation for each statement \n" ); document.write( ": \n" ); document.write( " the second angle is twice the measure of the first, \n" ); document.write( "B = 2A \n" ); document.write( "or we divide the equation by 2 and we have this form \n" ); document.write( "A = .5B \n" ); document.write( " and the third angle is three times the measure of the second. \n" ); document.write( "C = 3B \n" ); document.write( " : \n" ); document.write( "We know the sum of the 3 angles has to be 180 degrees \n" ); document.write( "A + B + C = 180 \n" ); document.write( "Replace A with .5B and C with 3B \n" ); document.write( ".5A + B + 3B = 180 \n" ); document.write( "4.5B = 180 \n" ); document.write( "B = 180/4.5 \n" ); document.write( "B = 40 degrees \n" ); document.write( ": \n" ); document.write( "\"Find the measure of the third angle\" \n" ); document.write( "We know that C = 3B, therefore \n" ); document.write( "C = 3(40) \n" ); document.write( "C - 120 degrees is the third angle \n" ); document.write( ": \n" ); document.write( ": \n" ); document.write( "We can confirm this by finding the 1st angle and see if the 3 angles add up 180 \n" ); document.write( "A = .5(40) \n" ); document.write( "A = 20 degrees \n" ); document.write( "20 + 40 + 120 = 180 \n" ); document.write( " |