document.write( "Question 1029748: Assume quadrilateral ABCD is inscribed in a circle. If $\"m%3CA+=+x%5E2\"$ , $\"m%3CB+=+9x+-+2\"$ , and $\"m%3CC+=+11x\"$ , find x and the measure of angle D. \n" ); document.write( "

Algebra.Com's Answer #644735 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Assume quadrilateral ABCD is inscribed in a circle. If $\"m%3CA+=+x%5E2\"$ , $\"m%3CB+=+9x+-+2\"$ , and $\"m%3CC+=+11x\"$ , find x and the measure of angle D.
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document.write( "If a quadrilateral is inscribed in a circle, then its opposite angles sum up to 180°.\r\n" );
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document.write( "In other words, If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.\r\n" );
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document.write( "I think if the teacher gave you this problem, you should be familiar with this fact. \r\n" );
document.write( "If not, you can read about it in the lesson A property of the angles of a quadrilateral inscribed in a circle in this site.\r\n" );
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document.write( "OK. Based on this fact, you can write an equation for the opposite angles A and C\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( " = .\r\n" );
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document.write( "Factor left side:\r\n" );
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document.write( "(x-9)*(x+20) = 0.\r\n" );
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document.write( "The only positive root is x = 9.\r\n" );
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document.write( "Hence, angle A is 81° and angle C is 11*9° = 99°. (which is not so important for us now).\r\n" );
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document.write( "What is really important, it is the fact that angle B is 9*9°-2° = 79°.\r\n" );
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document.write( "Then the opposite to B angle D = 180° - 79° = 101°.\r\n" );
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document.write( "Answer. Angle D has the measure of 101°.\r\n" );
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