document.write( "Question 1209450: A triangle ABC, where |AB| = |AC|, a line CD is drawn from angle C and intersects side AB at D, such that |AD| = |CD| = |BC|. Find the measure of angle A in degrees.\r
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Algebra.Com's Answer #848859 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "A triangle ABC, where |AB| = |AC|, a line CD is drawn from angle C and intersects side AB at D,
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\n" ); document.write( "\n" ); document.write( "            The solution and the answer  (72 degrees)  in the post by  @PChill is incorrect \r
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document.write( "Draw triangle ABC with |AB| = |AC| and everything else from the problem on the sheet of paper.\r\n" );
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document.write( "Let x be the measure of the angle A;\r\n" );
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document.write( "    y be the measure of the angle B.\r\n" );
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document.write( "Consider triangle ABC. It is isosceles, since |AB| = |AC|  (given).\r\n" );
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document.write( "                       Its \"base\" angle is y;  its \"vertex\" angle is x.\r\n" );
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document.write( "                       Therefore, x + 2y = 180°.    (1)\r\n" );
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document.write( "Consider triangle ADC. It is isosceles, since |AD| = |CD|  (given).\r\n" );
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document.write( "                       Its \"base\" angle is x;  its \"vertex\" angle is 180°-y   (from triangle BCD, which also is isosceles).\r\n" );
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document.write( "                       Therefore, 2x  + (180°-y) = 180°,\r\n" );
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document.write( "                       which implies  2x = y.       (2)\r\n" );
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document.write( "Now we have the system of two equations (1) and (2).\r\n" );
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document.write( "From (2), substitute y = 2x into equation (1).  You will get\r\n" );
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document.write( "    x + 2*(2x) = 180,\r\n" );
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document.write( "    x + 4x = 180,\r\n" );
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document.write( "      5x   = 180,\r\n" );
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document.write( "       x   = 180/5 = 36 degrees.\r\n" );
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document.write( "At this point, the problem is solved completely.\r\n" );
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document.write( "ANSER.  Angle A is 36 degrees.\r\n" );
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\n" ); document.write( "\n" ); document.write( "        Hello,  @math_tuitor2020,  please remove all your insinuations \r
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\n" ); document.write( "\n" ); document.write( "                                                    Jan. 20, 2025.\r
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