document.write( "Question 811345: Three angles of a hexagon are congruent. Find the other three angles if they are in the ratio of 1:2:4. \n" ); document.write( "
Algebra.Com's Answer #488736 by Edwin McCravy(20067) $\"\"$ $\"About$
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document.write( "The sum of the interior angles of a polygon is (n-2)180°\r\n" );
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document.write( "So the sum of the interior angles of a hexagon (which has n=6 sides)\r\n" );
document.write( "is (6-2)180° = (4)180° = 720°\r\n" );
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document.write( "Let the angles in the ratio 1:2:4 be x°, 2x° and 4x°\r\n" );
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document.write( "Let the three congruent angles each have value y°\r\n" );
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document.write( "So the 6 angles are\r\n" );
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document.write( "x°, 2x°, 4x°, y°, y°, y°\r\n" );
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document.write( "Then the sum of the 6 angles is\r\n" );
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document.write( "x° + 2x° + 4x° + y° + y° + y° = 720°\r\n" );
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document.write( "                      7x + 3y = 720 \r\n" );
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document.write( "So there are lots of possible answers.\r\n" );
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document.write( "For example if you choose x° to be 30° you will get\r\n" );
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document.write( "                     7(30) + 3y = 720\r\n" );
document.write( "                       210 + 3y = 720\r\n" );
document.write( "                             3y = 510\r\n" );
document.write( "                              y = 170\r\n" );
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document.write( "So the 6 angles will be\r\n" );
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document.write( " x°,  2x°,  4x°,   y°,   y°,   y°\r\n" );
document.write( "30°,  60°,  90°, 170°, 170°, 170°\r\n" );
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document.write( "But if you choose x to be 36° you will get\r\n" );
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document.write( "                     7(36) + 3y = 720\r\n" );
document.write( "                       252 + 3y = 720\r\n" );
document.write( "                             3y = 468\r\n" );
document.write( "                              y = 156\r\n" );
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document.write( " So the 6 angles will be:\r\n" );
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document.write( " x°,  2x°,  4x°,   y°,   y°,   y°\r\n" );
document.write( "36°,  72°, 108°, 156°, 156°, 156°\r\n" );
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document.write( "And if you choose x to be 42° you will get\r\n" );
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document.write( "                     7(42) + 3y = 720\r\n" );
document.write( "                       294 + 3y = 720\r\n" );
document.write( "                             3y = 426\r\n" );
document.write( "                              y = 142\r\n" );
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document.write( " So the 6 angles will be:\r\n" );
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document.write( " x°,  2x°,  4x°,   y°,   y°,   y°\r\n" );
document.write( "42°,  84°, 168°, 142°, 142°, 142°\r\n" );
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document.write( "So your problem has many many different answers.  \r\n" );
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document.write( "Did you leave something out?\r\n" );
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document.write( "Edwin
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