document.write( "Question 1196065: Question 1 options:
\n" ); document.write( "The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is fifteen more than the second. Find the measures of the three angles. \n" ); document.write( "

Algebra.Com's Answer #828752 by ikleyn(52847) $\"\"$ $\"About$

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\n" ); document.write( "Question 1 options:
\n" ); document.write( "The sum of the measures of the angles of a triangle is 180.
\n" ); document.write( "The sum of the measures of the second and third angles is three times
\n" ); document.write( "the measure of the first angle.
\n" ); document.write( "The third angle is fifteen more than the second.
\n" ); document.write( "Find the measures of the three angles.
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document.write( "Let the angles be x, y, and z (the degrees measures for the 1st, 2nd and 3rd).\r\n" );
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document.write( "Then\r\n" );
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document.write( "    x + y + z = 180 degrees.\r\n" );
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document.write( "Group them according the condition\r\n" );
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document.write( "    x + (y + z) = 180\r\n" );
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document.write( "Replace (y + z) by 3x, since it is given.  You will get\r\n" );
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document.write( "    x + 3x = 180\r\n" );
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document.write( "      4x   = 180\r\n" );
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document.write( "       x   = 180/4 = 45 degrees for the 1st angle.\r\n" );
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document.write( "Thus y + z = 180 - 45 = 135,  and z = y+15.\r\n" );
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document.write( "It gives  y + (y+15) = 135,  2y = 135-15 = 120,  y = 120/2 = 60 degrees for the 2nd angle.\r\n" );
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document.write( "Hence, z = 60+15 = 75 degrees.\r\n" );
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document.write( "ANSWER.  1st angle is 45 degrees;  2nd angle is 60 degrees;  3rd angle is 75 degrees.\r\n" );
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